A135350 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4).

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

Offset: 0

Author

Paul Curtz, Feb 16 2008

Keywords

• nonn

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).

Crossrefs

Cf. A117373.

Programs

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 *)

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)

Extensions

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