A133190 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3).

1, 3, 3, 5, 13, 27, 51, 101, 205, 411, 819, 1637, 3277, 6555, 13107, 26213, 52429, 104859, 209715, 419429, 838861, 1677723, 3355443, 6710885, 13421773, 26843547, 53687091, 107374181, 214748365, 429496731, 858993459, 1717986917, 3435973837

Offset

0,2

Links

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

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

Formula

From R. J. Mathar, Jan 13 2008: (Start)

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

a(n) = (4*2^n + (-1)^floor(n/2)*A010688(n))/5. (End)

a(n) = ((1 - 7*i)*i^n + 8*2^n + (1 + 7*i)*(-i)^n)/10, with n>=0 and i=sqrt(-1). - Paolo P. Lava, Jun 09 2008

Maple

A010688 := proc(n) if n mod 2 = 0 then 1; else 7; fi ; end:
A133190 := proc(n) (4*2^n+(-1)^floor(n/2)*A010688(n))/5 ; end:
seq(A133190(n), n=0..30) ; # R. J. Mathar, Jan 13 2008

Mathematica

LinearRecurrence[{2, -1, 2}, {1, 3, 3}, 40] (* Harvey P. Dale, Jun 22 2022 *)

Crossrefs

Sequence in context: A144419 A212322 A226921 * A052898 A183483 A218663

Adjacent sequences: A133187 A133188 A133189 * A133191 A133192 A133193

Keyword

nonn,easy

Author

Paul Curtz, Dec 17 2007

Status

approved