A332735 Numbers of graphs which are double triangle descendants of K_5 with four more vertices than triangles.

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

Offset

9,2

Comments

See Laradji, Mishna, Yeats paper for definition of double triangle descendants.

Links

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).

Formula

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.

Crossrefs

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

Keyword

nonn,easy

Author

Karen A. Yeats, Feb 21 2020

Status

approved