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