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 A277978 #31 Aug 23 2021 13:38:19 %S A277978 0,12,30,54,84,120,162,210,264,324,390,462,540,624,714,810,912,1020, %T A277978 1134,1254,1380,1512,1650,1794,1944,2100,2262,2430,2604,2784,2970, %U A277978 3162,3360,3564,3774,3990,4212,4440,4674,4914,5160,5412,5670,5934,6204,6480 %N A277978 a(n) = 3*n*(n+3). %C A277978 For n>= 3, a(n) is the second Zagreb index of the wheel graph with n+1 vertices. The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of g. %H A277978 Leo Tavares, <a href="/A277978/a277978_1.jpg">Illustration: Hexagonal Stars</a> %H A277978 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A277978 a(n) = 2 * A140091(n) = 3 * A028552(n) = 6 * A000096(n). %F A277978 G.f.: 6*x*(2-x)/(1-x)^3 %F A277978 a(n) = A003154(n+1) - A003215(n-1). See Hexagonal Stars illustration. - _Leo Tavares_, Aug 20 2021 %e A277978 a(3) = 54. Indeed, the wheel graph with 4 vertices consists of 6 edges, each connecting two vertices of degree 3. Then, the second Zagreb index is 6*3*3 = 54. %p A277978 seq(3*n*(n+3), n = 0 .. 45); %t A277978 A277978[n_] := 3 n (n + 3); Array[A277978, 45] (* _JungHwan Min_, Nov 08 2016 *) %o A277978 (PARI) a(n)=3*n*(n+3) \\ _Charles R Greathouse IV_, Jun 17 2017 %Y A277978 Cf. A000096, A028569, A140091. %K A277978 nonn,easy %O A277978 0,2 %A A277978 _Emeric Deutsch_, Nov 08 2016