

A304610


a(n) = 157*n  40 (n>=1).


2



117, 274, 431, 588, 745, 902, 1059, 1216, 1373, 1530, 1687, 1844, 2001, 2158, 2315, 2472, 2629, 2786, 2943, 3100, 3257, 3414, 3571, 3728, 3885, 4042, 4199, 4356, 4513, 4670, 4827, 4984, 5141, 5298, 5455, 5612, 5769, 5926, 6083, 6240
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OFFSET

1,1


COMMENTS

a(n) is the second Zagreb index of the polymer B[n,1], defined pictorially in the BodrozaPantic et al. reference (Fig. 4).
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 Mpolynomial of B[n,1] is M(B[n,1]; x,y) = 2*(2*n+1)*x^2*y^2 + 4*(n+1)*x^2*y^3 + (13*n8)*x^3*y^3.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
O. BodrozaPantic, I. Gutman, and S. J. Cyvin, Algebraic structure count of some nonbenzenoid conjugated polymers, ACH  Models in Chemistry, 133 (12), 2741, 1996.
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 (2,1).


FORMULA

From Colin Barker, May 18 2018: (Start)
G.f.: x*(117 + 40*x) / (1  x)^2.
a(n) = 2*a(n1)  a(n2) for n>2.
(End)


MAPLE

seq(157*n40, n = 1 .. 40);


MATHEMATICA

Table[157n40, {n, 40}] (* or *) LinearRecurrence[{2, 1}, {117, 274}, 40] (* Harvey P. Dale, Oct 13 2019 *)


PROG

(GAP) List([1..40], n>157*n40); # Muniru A Asiru, May 17 2018
(PARI) a(n) = 157*n  40; \\ Altug Alkan, May 18 2018
(PARI) Vec(x*(117 + 40*x) / (1  x)^2 + O(x^40)) \\ Colin Barker, May 18 2018


CROSSREFS

Cf. A304609.
Sequence in context: A063332 A063338 A304611 * A298047 A252861 A252854
Adjacent sequences: A304607 A304608 A304609 * A304611 A304612 A304613


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 17 2018


STATUS

approved



