A277982 a(n) = 12*n^2 + 10*n - 30.

-30, -8, 38, 108, 202, 320, 462, 628, 818, 1032, 1270, 1532, 1818, 2128, 2462, 2820, 3202, 3608, 4038, 4492, 4970, 5472, 5998, 6548, 7122, 7720, 8342, 8988, 9658, 10352, 11070, 11812, 12578, 13368, 14182, 15020, 15882, 16768, 17678, 18612, 19570

Offset

0,1

Comments

For n>=3, a(n) is the second Zagreb index of the uniform bow graph B[n]. 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 the graph. The uniform bow graph B[n] consists of two path graphs P[n] and an additional vertex joined by 2n edges to the vertices of the paths.

The M-polynomial of the uniform bow graph B[n] is M(B[n],x,y) = 4*x^2*y^3 + 4*x^2*y^{2*n} + (2*n-6)*x^3*y^3 + (2*n-4)*x^3*y^{2*n}.

Links

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

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

J. Jeba Jesintha and K. Ezhilarasi Hilda, All uniform bow graphs are graceful, Math. Comput. Sci., 9, 2015, 185-191.

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

Formula

O.g.f.: 2*(7*x - 3)*(2*x - 5)/(x - 1)^3.

E.g.f.: 2*(6*x^2 + 11*x - 15)*exp(x). - Bruno Berselli, Nov 11 2016

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Nov 11 2016

Maple

seq(12*n^2+10*n-30, n=0..40);

Mathematica

Table[12 n^2 + 10 n - 30, {n, 0, 50}] (* Vincenzo Librandi, Nov 11 2016 *)
LinearRecurrence[{3, -3, 1}, {-30, -8, 38}, 50] (* Harvey P. Dale, Apr 19 2020 *)

Prog

(Sage) [12*n^2+10*n-30 for n in range(50)] # Bruno Berselli, Nov 11 2016
(Magma) [12*n^2+10*n-30: n in [0..50]]; // Vincenzo Librandi, Nov 11 2016
(PARI) a(n)=12*n^2+10*n-30 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A277981.

Sequence in context: A040877 A265995 A040876 * A287921 A073401 A350085

Adjacent sequences: A277979 A277980 A277981 * A277983 A277984 A277985

Keyword

sign,easy

Author

Emeric Deutsch, Nov 10 2016

Status

approved