This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321307 #7 Feb 27 2025 10:34:26 %S A321307 5,10,41,98,257,537,1131,2116,3893,6665,11177,17867,28011,42419,63145, %T A321307 91586,130870,183230,253265,344373,463073,614332,807138,1048517, %U A321307 1350574,1722948,2181614,2739523,3417356,4232137 %N A321307 The number of connected weighted cubic graphs with weight n on 8 vertices. %C A321307 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. %H A321307 <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, 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). %F A321307 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)). %e A321307 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. %Y A321307 Cf. A026810 (4 vertices), A321306 (6 vertices). %K A321307 nonn,easy %O A321307 8,1 %A A321307 _R. J. Mathar_, Nov 03 2018