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 A321305 Triangle T(n,f): the number of signed cubic graphs on 2n vertices with f edges of the first sign. 2
 1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 1, 1, 2, 3, 8, 16, 21, 21, 16, 8, 3, 2, 5, 14, 57, 152, 313, 474, 551, 474, 313, 152, 57, 14, 5, 19, 91, 491, 1806, 5034, 10604, 17318, 22033, 22033, 17318, 10604, 5034, 1806, 491, 91, 19, 85, 706, 4981, 23791, 84575, 229078, 487020, 825127, 1127783, 1250632, 1127783, 825127, 487020, 229078, 84575, 23791, 4981, 706, 85 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS These are connected, undirected, simple cubic graphs where each edge is signed as either "+" or "-". Row n has 1+3n entries, 0<=f<=3n. The column f=0 (1, 0, 1, 2, 5,...) counts the cubic graphs (A002851). The column f=1 (0, 1, 3, 14, 91, 706,...) counts the edge-rooted cubic graphs. LINKS FORMULA T(n,f) = T(n,3*n-f). EXAMPLE The triangle starts: 0 vertices: 1 2 vertices: 0,0,0,0 4 vertices: 1,1,2,3,2,1,1 6 vertices: 2,3,8,16,21,21,16,8,3,2 8 vertices: 5,14,57,152,313,474,551,474,313,152,57,14,5 10 vertices: 19,91,491,1806,5034,10604,17318,22033,22033,17318,10604,5034,1806,491,91,19 CROSSREFS Cf. A002851 (first column), A321304 (signed vertices), A302939 (signed trees). Sequence in context: A105734 A076839 A092542 * A339178 A026552 A333271 Adjacent sequences:  A321302 A321303 A321304 * A321306 A321307 A321308 KEYWORD nonn,tabf AUTHOR R. J. Mathar, Nov 03 2018 STATUS approved

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Last modified August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)
The text passage is an entry from the Online Encyclopedia of Integer Sequences (OEIS) describing a specific integer sequence (A321305) related to signed cubic graphs. It includes a table of values, comments, formulas, and cross-references to related sequences.
no_question

the passage does not contain any mathematical questions or answers to questions. it is purely descriptive and provides information about a specific integer sequence.
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
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The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A321305 Triangle T(n,f): the number of signed cubic graphs on 2n vertices with f edges of the first sign. 2
 1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 1, 1, 2, 3, 8, 16, 21, 21, 16, 8, 3, 2, 5, 14, 57, 152, 313, 474, 551, 474, 313, 152, 57, 14, 5, 19, 91, 491, 1806, 5034, 10604, 17318, 22033, 22033, 17318, 10604, 5034, 1806, 491, 91, 19, 85, 706, 4981, 23791, 84575, 229078, 487020, 825127, 1127783, 1250632, 1127783, 825127, 487020, 229078, 84575, 23791, 4981, 706, 85 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS These are connected, undirected, simple cubic graphs where each edge is signed as either "+" or "-". Row n has 1+3n entries, 0<=f<=3n. The column f=0 (1, 0, 1, 2, 5,...) counts the cubic graphs (A002851). The column f=1 (0, 1, 3, 14, 91, 706,...) counts the edge-rooted cubic graphs. LINKS FORMULA T(n,f) = T(n,3*n-f). EXAMPLE The triangle starts: 0 vertices: 1 2 vertices: 0,0,0,0 4 vertices: 1,1,2,3,2,1,1 6 vertices: 2,3,8,16,21,21,16,8,3,2 8 vertices: 5,14,57,152,313,474,551,474,313,152,57,14,5 10 vertices: 19,91,491,1806,5034,10604,17318,22033,22033,17318,10604,5034,1806,491,91,19 CROSSREFS Cf. A002851 (first column), A321304 (signed vertices), A302939 (signed trees). Sequence in context: A105734 A076839 A092542 * A339178 A026552 A333271 Adjacent sequences:  A321302 A321303 A321304 * A321306 A321307 A321308 KEYWORD nonn,tabf AUTHOR R. J. Mathar, Nov 03 2018 STATUS approved

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Last modified August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)
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The text passage is an entry from the Online Encyclopedia of Integer Sequences (OEIS) describing a specific integer sequence (A321305) related to signed cubic graphs. It includes a table of values, comments, formulas, and cross-references to related sequences.

TYPE: NO_QUESTION

The passage does not contain any mathematical questions or answers to questions. It is purely descriptive and provides information about a specific integer sequence.