

A304609


a(n) = 114*n  20.


3



94, 208, 322, 436, 550, 664, 778, 892, 1006, 1120, 1234, 1348, 1462, 1576, 1690, 1804, 1918, 2032, 2146, 2260, 2374, 2488, 2602, 2716, 2830, 2944, 3058, 3172, 3286, 3400, 3514, 3628, 3742, 3856, 3970, 4084, 4198, 4312, 4426, 4540
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OFFSET

1,1


COMMENTS

a(n) is the first Zagreb index of the polymer B[n,1], defined pictorially in the BodrožaPantić et al. reference (Fig. 4).
a(n) is the first Zagreb index of the polymer B[n,2], defined pictorially in the BodrožaPantić et al. reference (Fig. 4).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums 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.
The Mpolynomial of B[n,2] is M(B[n,1]; x,y) = 2*(n+2)*x^2*y^2 + 8*n*x^2*y^3 + (11*n6)*x^3*y^3.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
O. BodrožaPantić, 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 Klavžar, 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 17 2018: (Start)
G.f.: 2*x*(47 + 10*x) / (1  x)^2.
a(n) = 2*a(n1)  a(n2) for n>2.
(End)


MAPLE

seq(114*n20, n = 1 .. 40);


PROG

(PARI) a(n) = 114*n  20; \\ Altug Alkan, May 16 2018
(PARI) Vec(2*x*(47 + 10*x) / (1  x)^2 + O(x^40)) \\ Colin Barker, May 17 2018
(GAP) List([1..80], n>114*n20); # Muniru A Asiru, May 17 2018


CROSSREFS

Cf. A304610, A304611.
Sequence in context: A050965 A044426 A044807 * A116109 A107412 A115996
Adjacent sequences: A304606 A304607 A304608 * A304610 A304611 A304612


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 16 2018


STATUS

approved



