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

Author

Paul Curtz, Dec 17 2007

Keywords

• nonn
• easy

Links

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

Programs

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 *)

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)