

A277982


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


1



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
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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 Mpolynomial 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*n6)*x^3*y^3 + (2*n4)*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.
J. Jeba Jesintha and K. Ezhilarasi Hilda, All uniform bow graphs are graceful, Math. Comput. Sci., 9, 2015, 185191.
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(n1)  3*a(n2) + a(n3).  Vincenzo Librandi, Nov 11 2016


MAPLE

seq(12*n^2+10*n30, n=0..40);


MATHEMATICA

Table[12 n^2 + 10 n  30, {n, 0, 50}] (* Vincenzo Librandi, Nov 11 2016 *)


PROG

(Sage) [12*n^2+10*n30 for n in xrange(50)] # Bruno Berselli, Nov 11 2016
(MAGMA) [12*n^2+10*n30: n in [0..50]]; // Vincenzo Librandi, Nov 11 2016
(PARI) a(n)=12*n^2+10*n30 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A277981.
Sequence in context: A040877 A265995 A040876 * A287921 A073401 A040875
Adjacent sequences: A277979 A277980 A277981 * A277983 A277984 A277985


KEYWORD

sign,easy


AUTHOR

Emeric Deutsch, Nov 10 2016


STATUS

approved



