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A321307
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The number of connected weighted cubic graphs with weight n on 8 vertices.
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1
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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
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OFFSET
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8,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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