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

Author

Karen A. Yeats, Feb 21 2020

Keywords

• nonn
• easy

Comments

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

Links

• 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).

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.

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.