

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
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OFFSET

0,2


COMMENTS

For n>=3, a(n) is the second Zagreb index of the doublewheel 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 doublewheel graph DW[n] consists of two cycles C[n], whose vertices are connected to an additional vertex.
The Mpolynomial of the doublewheel 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.
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: 6*x*(5x)/(1x)^3.
a(n) = 3*a(n1)  3*a(n2) + a(n3).
a(n) = 6*A014106(n).
a(n) = A152746(n+1)  6 = A154105(n)  7.  Omar E. Pol, May 08 2018


EXAMPLE

a(3) = 162. Indeed, the doublewheel graph DW[3] has 6 edges with endpoint degrees 3,3 and 6 edges with endpoint 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: 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



