A304514 a(n) = 33*2^n - 45 (n>=1).

21, 87, 219, 483, 1011, 2067, 4179, 8403, 16851, 33747, 67539, 135123, 270291, 540627, 1081299, 2162643, 4325331, 8650707, 17301459, 34602963, 69205971, 138411987, 276824019, 553648083, 1107296211, 2214592467, 4429184979, 8858370003, 17716740051, 35433480147, 70866960339, 141733920723, 283467841491, 566935683027, 1133871366099

Offset

1,1

Comments

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

Links

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

M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.

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

Formula

From Colin Barker, May 15 2018: (Start)

G.f.: 3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(33*2^n-45, n = 1 .. 40);

Mathematica

Rest@ CoefficientList[Series[3 x (7 + 8 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)
LinearRecurrence[{3, -2}, {21, 87}, 35] (* or *)
Array[33*2^# - 45 &, 35] (* Michael De Vlieger, May 15 2018 *)

Prog

(GAP) List([1..40], n->33*2^n-45); # Muniru A Asiru, May 15 2018
(PARI) a(n) = 33*2^n - 45; \\ Altug Alkan, May 15 2018
(PARI) Vec(3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

Crossrefs

Cf. A304513, A304515, A304516.

Sequence in context: A240518 A219850 A158540 * A219886 A211464 A268257

Adjacent sequences: A304511 A304512 A304513 * A304515 A304516 A304517

Keyword

nonn,easy

Author

Emeric Deutsch, May 15 2018

Status

approved