A304517 a(n) = 16*2^n - 11 (n>=1).

21, 53, 117, 245, 501, 1013, 2037, 4085, 8181, 16373, 32757, 65525, 131061, 262133, 524277, 1048565, 2097141, 4194293, 8388597, 16777205, 33554421, 67108853, 134217717, 268435445, 536870901, 1073741813, 2147483637, 4294967285, 8589934581, 17179869173, 34359738357, 68719476725, 137438953461, 274877906933, 549755813877

Offset

1,1

Comments

a(n) is the number of edges of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

A. Madanshekaf and M. Moradi, The first geometric-arithmetic index of some nanostar dendrimers, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.

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

Formula

From Colin Barker, May 15 2018: (Start)

G.f.: x*(21 - 10*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(16*2^n-11, n = 1 .. 40);

Mathematica

Rest@ CoefficientList[Series[x (21 - 10 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)
LinearRecurrence[{3, -2}, {21, 53}, 35] (* or *)
Array[16*2^# - 11 &, 35] (* Michael De Vlieger, May 15 2018 *)

Prog

(GAP) List([1..40], n->16*2^n-11); # Muniru A Asiru, May 15 2018
(PARI) Vec(x*(21 - 10*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304518, A304518.

First bisection of A164096 without 5. First column of the table in A224701.

Sequence in context: A043913 A280914 A347837 * A007796 A211460 A354160

Adjacent sequences: A304514 A304515 A304516 * A304518 A304519 A304520

Keyword

nonn,easy

Author

Emeric Deutsch, May 15 2018

Status

approved