A321307 The number of connected weighted cubic graphs with weight n on 8 vertices.

5, 10, 41, 98, 257, 537, 1131, 2116, 3893, 6665, 11177, 17867, 28011, 42419, 63145, 91586, 130870, 183230, 253265, 344373, 463073, 614332, 807138, 1048517, 1350574, 1722948, 2181614, 2739523, 3417356, 4232137

Offset: 8

Author

R. J. Mathar, Nov 03 2018

Keywords

• nonn
• easy

Comments

Each vertex of the 5 simple cubic graphs is assigned an integer number (weight) >=1. The weight of the graph is the sum of the weights of the vertices.

Examples

			a(8)=5 because there are 5 cubic graphs (see A002851), and if the weight is the same as the number of vertices, there is one case for each.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1,-2,5,-5,4,-3,-1,6,-6,4,-6,6,-1,-3,4,-5,5,-2,1,-1,-2,3,-1).

Crossrefs

Cf. A026810 (4 vertices), A321306 (6 vertices).

Formula

G.f.: x^8*(x^18 +10*x^16 +5*x^15 +37*x^14 +8*x^13 +75*x^12 +16*x^11 +103*x^10 +16*x^9 +108*x^8 +13*x^7 +86*x^6 +3*x^5 +50*x^ 4+21*x^2 -5*x +5)/((-1+x)^8* (1+x)^4 *(x^2+x+1)^2 *(x^2-x+1) *(1+x^2)^2 *(1+x^4)).