

A120718


Expansion of 3*x/(1  2*x^2  2*x + x^3).


1



0, 3, 6, 18, 45, 120, 312, 819, 2142, 5610, 14685, 38448, 100656, 263523, 689910, 1806210, 4728717, 12379944, 32411112, 84853395, 222149070, 581593818, 1522632381, 3986303328, 10436277600, 27322529475, 71531310822, 187271402994, 490282898157, 1283577291480
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OFFSET

0,2


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,1).


FORMULA

a(n) = 3*A001654(n).  Arkadiusz Wesolowski, Sep 15 2012
From Colin Barker, Oct 01 2016: (Start)
a(n) = 2*a(n1)+2*a(n2)a(n3) for n>2.
a(n) = (3)*(2^(1n)*((1)^n*2^(1+n)+(3sqrt(5))^n*(1+sqrt(5))(1+sqrt(5))*(3+sqrt(5))^n))/5.
(End)


MATHEMATICA

LinearRecurrence[{2, 2, 1}, {0, 3, 6}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)


PROG

(PARI) a(n) = round((3)*(2^(1n)*((1)^n*2^(1+n)+(3sqrt(5))^n*(1+sqrt(5))(1+sqrt(5))*(3+sqrt(5))^n))/5) \\ Colin Barker, Oct 01 2016
(PARI) concat(0, Vec(3*x/(12*x^22*x+x^3) + O(x^40))) \\ Colin Barker, Oct 01 2016


CROSSREFS

Cf. A000045, A072845.
Sequence in context: A007990 A197050 A121188 * A032120 A115344 A223044
Adjacent sequences: A120715 A120716 A120717 * A120719 A120720 A120721


KEYWORD

nonn,easy


AUTHOR

Roger L. Bagula, Aug 13 2006


EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Sep 15 2012


STATUS

approved



