A277980 a(n) = 12*n^2 + 18*n.

0, 30, 84, 162, 264, 390, 540, 714, 912, 1134, 1380, 1650, 1944, 2262, 2604, 2970, 3360, 3774, 4212, 4674, 5160, 5670, 6204, 6762, 7344, 7950, 8580, 9234, 9912, 10614, 11340, 12090, 12864, 13662, 14484, 15330, 16200, 17094, 18012, 18954, 19920

Offset

0,2

Comments

For n >= 3, a(n) is the second Zagreb index of the double-wheel graph DW[n]. The second Zagreb index of a simple connected graph g is the sum of the degree products d(i) d(j) over all edges ij of g.

The double-wheel graph DW[n] consists of two cycles C[n], whose vertices are connected to an additional vertex.

The M-polynomial of the double-wheel graph DW[n] is M(DW[n],x,y) = 2*n*x^3*y^3 + 2*n*x^3*y^{2*n}.

Links

Table of n, a(n) for n=0..40.

Emeric Deutsch and Sandi Klavžar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2 (2015), 93-102.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: 6*x*(5-x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = 6*A014106(n).

a(n) = A152746(n+1) - 6 = A154105(n) - 7. - Omar E. Pol, May 08 2018

From Amiram Eldar, Jun 22 2026: (Start)

Sum_{n>=1} 1/a(n) = 4/27 - log(2)/9.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2/27 - Pi/36 + log(2)/18. (End)

Example

a(3) = 162. Indeed, the double-wheel graph DW[3] has 6 edges with end-point degrees 3,3 and 6 edges with end-point degrees 3,6. Then the second Zagreb index is 6*9 + 6*18 = 162.

Maple

seq(12*n^2+18*n, n = 0 .. 50);

Mathematica

Table[12 n^2 + 18 n, {n, 0, 45}] (* Vincenzo Librandi, Nov 09 2016 *)

Prog

(Magma) [12*n^2+18*n: n in [0..40]]; // Vincenzo Librandi, Nov 09 2016
(PARI) a(n)=12*n^2+18*n \\ Charles R Greathouse IV, Nov 09 2016

Crossrefs

Cf. A014106, A152746, A154105, A277979.

First bisection of A277978.

After 0, subsequence of A255265.

Sequence in context: A353176 A155461 A165772 * A241025 A326309 A326838

Adjacent sequences: A277977 A277978 A277979 * A277981 A277982 A277983

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 08 2016

Status

approved