A131370 - OEIS

A131370

a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.

3, 2, 0, 0, 4, 12, 24, 44, 84, 168, 340, 684, 1368, 2732, 5460, 10920, 21844, 43692, 87384, 174764, 349524, 699048, 1398100, 2796204, 5592408, 11184812, 22369620, 44739240, 89478484, 178956972, 357913944, 715827884, 1431655764, 2863311528

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OFFSET

0,1

COMMENTS

Sequence is identical to its third differences. Binomial transform of 3, -1, -1, 3, -1, -1, 3, -1, -1, ... .

LINKS

Table of n, a(n) for n=0..33.

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

FORMULA

a(n) = 2^n/3 + (8/3)cos(n*Pi/3). - Emeric Deutsch, Oct 15 2007

G.f.: -(3-7*x+3*x^2)/(2*x-1)/(x^2-x+1). - R. J. Mathar, Nov 14 2007

a(n) = 2*A086953(n-1) for n>0. - Rick L. Shepherd, Aug 02 2017

MAPLE

seq((1/3)*2^n+8*cos((1/3)*n*Pi)*1/3, n=0..33); # Emeric Deutsch, Oct 15 2007

MATHEMATICA

a = {3, 2, 0}; Do[AppendTo[a, 3*a[[ -1]] - 3*a[[ -2]] + 2*a[[ -3]]], {60}]; a (* Stefan Steinerberger, Oct 04 2007 *)

CROSSREFS

Cf. A086953.

Sequence in context: A292260 A322114 A062787 * A261180 A062707 A160230

Adjacent sequences: A131367 A131368 A131369 * A131371 A131372 A131373

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 30 2007

EXTENSIONS

More terms from Stefan Steinerberger, Oct 04 2007

STATUS

approved