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A304513 a(n) = 57*2^(n-1) - 38 (n >= 1). 4
19, 76, 190, 418, 874, 1786, 3610, 7258, 14554, 29146, 58330, 116698, 233434, 466906, 933850, 1867738, 3735514, 7471066, 14942170, 29884378, 59768794, 119537626, 239075290, 478150618, 956301274, 1912602586, 3825205210, 7650410458, 15300820954, 30601641946, 61203283930, 122406567898, 244813135834, 489626271706 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the number of vertices 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.: 19*x*(1 + x) / ((1 - x)*(1 - 2*x)).

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

(End)

MAPLE

seq(57*2^(n-1)-38, n = 1 .. 40);

MATHEMATICA

Rest@ CoefficientList[Series[19 x (1 + x)/((1 - x) (1 - 2 x)), {x, 0, 31}], x] (* or *)

LinearRecurrence[{3, -2}, {19, 76}, 31] (* or *)

Array[57*2^(# - 1) - 38 &, 31] (* Michael De Vlieger, May 15 2018 *)

PROG

(GAP) List([1..40], n->57*2^(n-1)-38); # Muniru A Asiru, May 15 2018

(PARI) Vec(19*x*(1 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018

CROSSREFS

Cf. A304514, A304515, A304516.

Sequence in context: A159997 A073566 A244631 * A041698 A098467 A041700

Adjacent sequences:  A304510 A304511 A304512 * A304514 A304515 A304516

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 15 2018

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)