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A321307 The number of connected weighted cubic graphs with weight n on 8 vertices. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 03 2018
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)