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A304514 a(n) = 33*2^n - 45 (n>=1). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 10 22:31 EDT 2021. Contains 342856 sequences. (Running on oeis4.)