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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 (list; graph; refs; listen; history; text; internal format)
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(n-1)+2*a(n-2)-a(n-3) for n>2.

a(n) = (-3)*(2^(-1-n)*((-1)^n*2^(1+n)+(3-sqrt(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^(-1-n)*((-1)^n*2^(1+n)+(3-sqrt(5))^n*(-1+sqrt(5))-(1+sqrt(5))*(3+sqrt(5))^n))/5) \\ Colin Barker, Oct 01 2016

(PARI) concat(0, Vec(3*x/(1-2*x^2-2*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

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Last modified February 19 20:48 EST 2018. Contains 299357 sequences. (Running on oeis4.)