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A332735
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Numbers of graphs which are double triangle descendants of K_5 with four more vertices than triangles.
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0
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1, 6, 15, 34, 61, 106, 162, 246, 342, 477, 626, 825, 1039, 1314, 1606, 1970, 2352, 2817, 3302, 3881, 4481, 5186, 5914, 6758, 7626, 8621, 9642, 10801, 11987, 13322, 14686, 16210, 17764, 19489, 21246, 23185, 25157, 27322, 29522, 31926, 34366, 37021, 39714, 42633, 45591, 48786
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OFFSET
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9,2
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COMMENTS
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See Laradji, Mishna, Yeats paper for definition of double triangle descendants.
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LINKS
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Table of n, a(n) for n=9..54.
Mohamed Laradji, Marni Mishna, and Karen Yeats, Some results on double triangle descendants of K_5, arXiv:1904.06923 [math.CO], 2019.
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,-1).
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FORMULA
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G.f.: x^9*(1 + 4*x + 3*x^2 + 6*x^3 + 3*x^4 + 4*x^5 + 4*x^7 - 3*x^8 + 3*x^9 - x^10 + x^11)/((1 - x)^4*(1 + x)^2*(1 + x^2)). See Laradji, Mishna, Yeats paper for proof.
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CROSSREFS
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Double triangle descendants of K_5 with three more vertices than triangles is A007980. Double triangle descendants of K_5 with two more vertices than triangles is A008619. Double triangle descendants of K_5 with one more vertex than triangles is A000007. Double triangle descendants of K_5 with the same number of vertices as triangles is A000012.
Sequence in context: A265395 A350596 A232604 * A120849 A358210 A338053
Adjacent sequences: A332732 A332733 A332734 * A332736 A332737 A332738
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KEYWORD
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nonn,easy
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AUTHOR
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Karen A. Yeats, Feb 21 2020
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STATUS
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approved
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