A304613 a(n) = 87*2^n - 45.

42, 129, 303, 651, 1347, 2739, 5523, 11091, 22227, 44499, 89043, 178131, 356307, 712659, 1425363, 2850771, 5701587, 11403219, 22806483, 45613011, 91226067, 182452179, 364904403, 729808851, 1459617747, 2919235539, 5838471123, 11676942291, 23353884627, 46707769299

Offset

0,1

Comments

a(n) is the number of edges of the nanostar dendrimer NS[n] from the Mirzargar reference.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

M. Mirzargar, PI, Szeged and edge Szeged polynomials of a dendrimer nanostar, MATCH, Commun. Math. Comput. Chem. 62, 2009, 363-370.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Colin Barker, May 17 2018: (Start)

G.f.: 3*(14 + x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>1. (End)

Maple

seq(87*2^n-45, n = 0 .. 40);

Mathematica

87*2^Range[0, 50] - 45 (* Paolo Xausa, Jul 31 2024 *)

Prog

(GAP) List([0..40], n->87*2^n-45); # Muniru A Asiru, May 17 2018
(PARI) a(n) = 87*2^n - 45; \\ Altug Alkan, May 17 2018
(PARI) Vec(3*(14 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 17 2018

Crossrefs

Cf. A304612, A304614, A304615.

Sequence in context: A261995 A298236 A299362 * A005557 A244102 A045088

Adjacent sequences: A304610 A304611 A304612 * A304614 A304615 A304616

Keyword

nonn,easy

Author

Emeric Deutsch, May 16 2018

Status

approved