A277978 a(n) = 3*n*(n+3).

0, 12, 30, 54, 84, 120, 162, 210, 264, 324, 390, 462, 540, 624, 714, 810, 912, 1020, 1134, 1254, 1380, 1512, 1650, 1794, 1944, 2100, 2262, 2430, 2604, 2784, 2970, 3162, 3360, 3564, 3774, 3990, 4212, 4440, 4674, 4914, 5160, 5412, 5670, 5934, 6204, 6480

Offset: 0

Author

Emeric Deutsch, Nov 08 2016

Keywords

• nonn
• easy

Comments

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.

Examples

			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.
		

Links

• Leo Tavares, Illustration: Hexagonal Stars
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000096, A028569, A140091.

Programs

Maple

seq(3*n*(n+3), n = 0 .. 45);

Mathematica

A277978[n_] := 3 n (n + 3); Array[A277978, 45] (* JungHwan Min, Nov 08 2016 *)

PARI

a(n)=3*n*(n+3) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 2 * A140091(n) = 3 * A028552(n) = 6 * A000096(n).

G.f.: 6*x*(2-x)/(1-x)^3

a(n) = A003154(n+1) - A003215(n-1). See Hexagonal Stars illustration. - Leo Tavares, Aug 20 2021