A191497 a(n+1) = 2*a(n) + A014017(n+5), a(0) = 0.

0, 0, 0, 0, 1, 2, 4, 8, 15, 30, 60, 120, 241, 482, 964, 1928, 3855, 7710, 15420, 30840, 61681, 123362, 246724, 493448, 986895, 1973790, 3947580, 7895160, 15790321, 31580642, 63161284, 126322568, 252645135

Offset

0,6

Links

Table of n, a(n) for n=0..32.

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

Formula

a(n+4) = 2^n - a(n).

a(n) = 2*a(n-1) - a(n-4) + 2*a(n-5).

a(4*n+4) = 16*a(4*n) + (-1)^n.

G.f.: -x^4 / ((2*x-1)*(x^4+1)). - R. J. Mathar, Jun 23 2011

a(n) = (2^n - (-1)^floor(n/4)*A133145(n))/17. - R. J. Mathar, Jun 23 2011

Maple

A191497 := proc(n): if n=0 then 0 else A191497(n) := 2*A191497(n-1) + A014017(n+4) fi: end: A014017 := proc(n): (1/8)*(-(n mod 8)-((n+3) mod 8)+((n+4) mod 8)+((n+7) mod 8)) end: seq(A191497(n), n=0..32); # Johannes W. Meijer, Jun 28 2011

Mathematica

LinearRecurrence[{2, 0, 0, -1, 2}, {0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 19 2013 *)

Crossrefs

Sequence in context: A251742 A251750 A251764 * A052325 A302774 A300520

Adjacent sequences: A191494 A191495 A191496 * A191498 A191499 A191500

Keyword

nonn,easy

Author

Paul Curtz, Jun 03 2011

Status

approved