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A135350 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). 2
0, 1, 3, 8, 15, 29, 56, 113, 227, 456, 911, 1821, 3640, 7281, 14563, 29128, 58255, 116509, 233016, 466033, 932067, 1864136, 3728271, 7456541, 14913080, 29826161, 59652323, 119304648, 238609295, 477218589, 954437176, 1908874353, 3817748707 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

FORMULA

From R. J. Mathar, Feb 19 2008: (Start)

O.g.f.: (1/9)*( -3*(x+2)/(x^2-x+1) - 8/(2*x-1) - 2/(x+1) ).

a(n) = (1/9)*( 2*(-1)^(n+1) + 2^(n+3) + 3*A117373(n+1) ). (End)

a(n) = -(1/3)*{1/2-(1/2)*I*sqrt(3)}^n-(2/9)*(-1)^n-(1/3)*{1/2+(1/2)*I*sqrt(3)}^n+(8/9)*2^n-(2/9) *I*{1/2-(1/2)*I*sqrt(3)}^n*sqrt(3)+(2/9)*I*{1/2+(1/2)*I*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1). - Paolo P. Lava, Jun 09 2008

MAPLE

A117373 := proc(n) coeftayl( (1-3*x)/(1-x+x^2), x=0, n) ; end: A135350 := proc(n) 2*(-1)^(n+1)/9+2^(n+3)/9+A117373(n+1)/3 ; end: seq(A135350(n), n=0..10) ; # R. J. Mathar, Feb 19 2008

MATHEMATICA

LinearRecurrence[{2, 0, -1, 2}, {0, 1, 3, 8}, 25] (* G. C. Greubel, Oct 11 2016 *)

CROSSREFS

Sequence in context: A015631 A116686 A317252 * A068038 A196087 A295735

Adjacent sequences:  A135347 A135348 A135349 * A135351 A135352 A135353

KEYWORD

nonn

AUTHOR

Paul Curtz, Feb 16 2008

EXTENSIONS

More terms from R. J. Mathar, Feb 19 2008

STATUS

approved

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Last modified August 6 15:41 EDT 2020. Contains 336253 sequences. (Running on oeis4.)