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

8,1

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.

Links

Table of n, a(n) for n=8..37.

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).

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)).

Example

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.

Crossrefs

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

Sequence in context: A038070 A364738 A136138 * A270288 A271805 A269812

Adjacent sequences: A321304 A321305 A321306 * A321308 A321309 A321310

Keyword

nonn,easy

Author

R. J. Mathar, Nov 03 2018

Status

approved