A305155 a(n) = 28*2^n - 15.

13, 41, 97, 209, 433, 881, 1777, 3569, 7153, 14321, 28657, 57329, 114673, 229361, 458737, 917489, 1834993, 3670001, 7340017, 14680049, 29360113, 58720241, 117440497, 234881009, 469762033, 939524081, 1879048177, 3758096369, 7516192753, 15032385521, 30064771057, 60129542129, 120259084273, 240518168561

Offset

0,1

Comments

a(n) is the number of edges in the nanostar dendrimer G(n), defined pictorially in the Darafsheh et al. reference (see Fig. 1, where G(2) is shown).

References

M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.

Links

Muniru A Asiru, Table of n, a(n) for n = 0..700

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

Formula

From Colin Barker, May 28 2018: (Start)

G.f.: (13 + 2*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(28*2^n-15, n = 0..40);

Mathematica

28*2^Range[0, 40]-15 (* or *) LinearRecurrence[{3, -2}, {13, 41}, 40] (* Harvey P. Dale, Dec 02 2018 *)

Prog

(PARI) Vec((13 + 2*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 28 2018
(GAP) List([0..40], n->28*2^n-15); # Muniru A Asiru, May 28 2018

Crossrefs

Cf. A226264, A305156, A305157.

Sequence in context: A123972 A167585 A141970 * A355965 A231885 A167240

Adjacent sequences: A305152 A305153 A305154 * A305156 A305157 A305158

Keyword

nonn,easy

Author

Emeric Deutsch, May 28 2018

Status

approved