A304172 a(n) = 99*2^n - 45 (n>=0).

54, 153, 351, 747, 1539, 3123, 6291, 12627, 25299, 50643, 101331, 202707, 405459, 810963, 1621971, 3243987, 6488019, 12976083, 25952211, 51904467, 103808979, 207618003, 415236051, 830472147, 1660944339, 3321888723, 6643777491, 13287555027, 26575110099, 53150220243, 106300440531, 212600881107, 425201762259

Offset

0,1

Comments

a(n) is the number of edges in the N-branched phenylacetylene NSB[n], shown pictorially in the Yarahmadi reference (for n=2).

Links

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

Z. Yarahmadi and G. H. Fath-Tabar, The Wiener, Szeged, PI, Vertex PI, the first and second Zagreb indices of N-branched phenylacetylenes dendrimers, MATCH: Commun. Math. Comput. Chem, 65, 2011, 201-208.

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

Formula

From Colin Barker, May 10 2018: (Start)

G.f.: 9*(6 - x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(99*2^n-45, n = 0 .. 35);

Prog

(PARI) Vec(9*(6 - x) / ((1 - x)*(1 - 2*x)) + O(x^30)) \\ Colin Barker, May 10 2018
(GAP) List([0..40], n->99*2^n-45); # Muniru A Asiru, May 10 2018

Crossrefs

Cf. A304171.

Sequence in context: A108780 A057396 A286836 * A044386 A044767 A250792

Adjacent sequences: A304169 A304170 A304171 * A304173 A304174 A304175

Keyword

nonn,easy

Author

Emeric Deutsch, May 10 2018

Status

approved