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 A131118 a(4n) = -n^2, a(4n+1) = n^2, a(4n+2) = 1-n^2, a(4n+3) = n*(n+1). 2
 0, 0, 1, 0, -1, 1, 0, 2, -4, 4, -3, 6, -9, 9, -8, 12, -16, 16, -15, 20, -25, 25, -24, 30, -36, 36, -35, 42, -49, 49, -48, 56, -64, 64, -63, 72, -81, 81, -80, 90, -100, 100, -99, 110, -121, 121, -120, 132, -144, 144, -143, 156, -169, 169, -168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Up to signs, the first differences are in A131804. - R. J. Mathar, Mar 17 2009 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA From R. J. Mathar, Mar 17 2009: (Start) a(n) = -2*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-5) +2*a(n-6) +2*a(n-7) +a(n-8). G.f.: x^2*(1+x^2+x^3+2*x)/((1-x)*(1+x^2)^2*(1+x)^3). (End) a(n) = ((-2*n^2+4*n+7)*(-1)^n - 2*((n+4)+(n+2)*(-1)^n)*i^(n*(n+1))+5)/32, where i=sqrt(-1). - Bruno Berselli, Mar 27 2012 MAPLE seq(((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32, n=0..60); # G. C. Greubel, Nov 18 2019 MATHEMATICA Table[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial[n+1, 2] +5)/32, {n, 0, 60}] (* G. C. Greubel, Nov 18 2019 *) PROG (PARI) a(n) = ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32; \\ G. C. Greubel, Nov 18 2019 (Magma) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1, 2) +5)/32: n in [0..60]]; // G. C. Greubel, Nov 18 2019 (Sage) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32 for n in (0..60)] # G. C. Greubel, Nov 18 2019 (GAP) List([0..60], n-> ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1, 2) +5)/32 ); # G. C. Greubel, Nov 18 2019 CROSSREFS Sequence in context: A135359 A098217 A151846 * A140765 A097541 A151819 Adjacent sequences: A131115 A131116 A131117 * A131119 A131120 A131121 KEYWORD sign,easy AUTHOR Paul Curtz, Sep 24 2007 EXTENSIONS More terms from Sean A. Irvine, Mar 13 2011 STATUS approved

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Last modified February 23 02:31 EST 2024. Contains 370265 sequences. (Running on oeis4.)
The text passage is a detailed entry from the Online Encyclopedia of Integer Sequences (OEIS) describing a specific integer sequence, its properties, and various formulas and code snippets for generating the sequence.
no_question

the passage does not contain any explicit mathematical questions or word problems. it is purely descriptive and provides information about the sequence, its definition, and methods to compute it.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A131118 a(4n) = -n^2, a(4n+1) = n^2, a(4n+2) = 1-n^2, a(4n+3) = n*(n+1). 2
 0, 0, 1, 0, -1, 1, 0, 2, -4, 4, -3, 6, -9, 9, -8, 12, -16, 16, -15, 20, -25, 25, -24, 30, -36, 36, -35, 42, -49, 49, -48, 56, -64, 64, -63, 72, -81, 81, -80, 90, -100, 100, -99, 110, -121, 121, -120, 132, -144, 144, -143, 156, -169, 169, -168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Up to signs, the first differences are in A131804. - R. J. Mathar, Mar 17 2009 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA From R. J. Mathar, Mar 17 2009: (Start) a(n) = -2*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-5) +2*a(n-6) +2*a(n-7) +a(n-8). G.f.: x^2*(1+x^2+x^3+2*x)/((1-x)*(1+x^2)^2*(1+x)^3). (End) a(n) = ((-2*n^2+4*n+7)*(-1)^n - 2*((n+4)+(n+2)*(-1)^n)*i^(n*(n+1))+5)/32, where i=sqrt(-1). - Bruno Berselli, Mar 27 2012 MAPLE seq(((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32, n=0..60); # G. C. Greubel, Nov 18 2019 MATHEMATICA Table[((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial[n+1, 2] +5)/32, {n, 0, 60}] (* G. C. Greubel, Nov 18 2019 *) PROG (PARI) a(n) = ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32; \\ G. C. Greubel, Nov 18 2019 (Magma) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1, 2) +5)/32: n in [0..60]]; // G. C. Greubel, Nov 18 2019 (Sage) [((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^binomial(n+1, 2) +5)/32 for n in (0..60)] # G. C. Greubel, Nov 18 2019 (GAP) List([0..60], n-> ((7+4*n-2*n^2)*(-1)^n -2*((n+4)+(n+2)*(-1)^n)*(-1)^Binomial(n+1, 2) +5)/32 ); # G. C. Greubel, Nov 18 2019 CROSSREFS Sequence in context: A135359 A098217 A151846 * A140765 A097541 A151819 Adjacent sequences: A131115 A131116 A131117 * A131119 A131120 A131121 KEYWORD sign,easy AUTHOR Paul Curtz, Sep 24 2007 EXTENSIONS More terms from Sean A. Irvine, Mar 13 2011 STATUS approved

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Last modified February 23 02:31 EST 2024. Contains 370265 sequences. (Running on oeis4.)
user
The text passage is a detailed entry from the Online Encyclopedia of Integer Sequences (OEIS) describing a specific integer sequence, its properties, and various formulas and code snippets for generating the sequence.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical questions or word problems. It is purely descriptive and provides information about the sequence, its definition, and methods to compute it.