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A277980 a(n) = 12*n^2 + 18*n. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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).

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, A277979.

Sequence in context: A044549 A155461 A165772 * A241025 A098996 A130862

Adjacent sequences:  A277977 A277978 A277979 * A277981 A277982 A277983

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 08 2016

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.