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 A282079 Number of n-element subsets of [n+2] having an even sum. 2
 1, 1, 2, 6, 9, 9, 12, 20, 25, 25, 30, 42, 49, 49, 56, 72, 81, 81, 90, 110, 121, 121, 132, 156, 169, 169, 182, 210, 225, 225, 240, 272, 289, 289, 306, 342, 361, 361, 380, 420, 441, 441, 462, 506, 529, 529, 552, 600, 625, 625, 650, 702, 729, 729, 756, 812, 841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1). FORMULA G.f.: -(x^4-2*x^3+4*x^2-2*x+1)/((x^2+1)^2*(x-1)^3). a(n) = A282011(n+2,n). a(n) = (2*(1+n)*(2+n) - i*(-i)^n*((1+2*i)+(1+i)*n) + i^n*((2+i)+(1+i)*n))/8 where i=sqrt(-1). - Colin Barker, Feb 06 2017 EXAMPLE a(3) = 6: {1,2,3}, {1,2,5}, {1,3,4}, {1,4,5}, {2,3,5}, {3,4,5}. a(4) = 9: {1,2,3,4}, {1,2,3,6}, {1,2,4,5}, {1,2,5,6}, {1,3,4,6}, {1,4,5,6}, {2,3,4,5}, {2,3,5,6}, {3,4,5,6}. PROG (PARI) Vec(-(x^4-2*x^3+4*x^2-2*x+1) / ((x^2+1)^2*(x-1)^3) + O(x^90)) \\ Colin Barker, Feb 06 2017 CROSSREFS Cf. A282011. Sequence in context: A263178 A198230 A263495 * A121248 A268677 A108370 Adjacent sequences: A282076 A282077 A282078 * A282080 A282081 A282082 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Feb 05 2017 STATUS approved

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Last modified May 22 09:57 EDT 2024. Contains 372745 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 related information.
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the passage does not contain any mathematical questions or answers to such questions. it is purely descriptive and provides information about the sequence a282079, including its definition, generating function, and examples.
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The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A282079 Number of n-element subsets of [n+2] having an even sum. 2
 1, 1, 2, 6, 9, 9, 12, 20, 25, 25, 30, 42, 49, 49, 56, 72, 81, 81, 90, 110, 121, 121, 132, 156, 169, 169, 182, 210, 225, 225, 240, 272, 289, 289, 306, 342, 361, 361, 380, 420, 441, 441, 462, 506, 529, 529, 552, 600, 625, 625, 650, 702, 729, 729, 756, 812, 841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1). FORMULA G.f.: -(x^4-2*x^3+4*x^2-2*x+1)/((x^2+1)^2*(x-1)^3). a(n) = A282011(n+2,n). a(n) = (2*(1+n)*(2+n) - i*(-i)^n*((1+2*i)+(1+i)*n) + i^n*((2+i)+(1+i)*n))/8 where i=sqrt(-1). - Colin Barker, Feb 06 2017 EXAMPLE a(3) = 6: {1,2,3}, {1,2,5}, {1,3,4}, {1,4,5}, {2,3,5}, {3,4,5}. a(4) = 9: {1,2,3,4}, {1,2,3,6}, {1,2,4,5}, {1,2,5,6}, {1,3,4,6}, {1,4,5,6}, {2,3,4,5}, {2,3,5,6}, {3,4,5,6}. PROG (PARI) Vec(-(x^4-2*x^3+4*x^2-2*x+1) / ((x^2+1)^2*(x-1)^3) + O(x^90)) \\ Colin Barker, Feb 06 2017 CROSSREFS Cf. A282011. Sequence in context: A263178 A198230 A263495 * A121248 A268677 A108370 Adjacent sequences: A282076 A282077 A282078 * A282080 A282081 A282082 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Feb 05 2017 STATUS approved

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Last modified May 22 09:57 EDT 2024. Contains 372745 sequences. (Running on oeis4.)
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The text passage is a detailed entry from the Online Encyclopedia of Integer Sequences (OEIS) describing a specific integer sequence, its properties, and related information.

TYPE: NO_QUESTION

The passage does not contain any mathematical questions or answers to such questions. It is purely descriptive and provides information about the sequence A282079, including its definition, generating function, and examples.