A221049 Expansion of (1+2*x+3*x^2-x^3)/((1-x)*(1+x)*(1-2*x)*(1+2*x)).

1, 2, 8, 9, 36, 37, 148, 149, 596, 597, 2388, 2389, 9556, 9557, 38228, 38229, 152916, 152917, 611668, 611669, 2446676, 2446677, 9786708, 9786709, 39146836, 39146837, 156587348, 156587349, 626349396, 626349397, 2505397588, 2505397589, 10021590356, 10021590357

Offset: 0

Author

Philippe Deléham, Apr 14 2013

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 5, 0, -4).

Crossrefs

Cf. A083597, A206374.

Programs

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {1, 2, 8, 9}, 40] (* T. D. Noe, Apr 17 2013 *)

Formula

a(n) = a(n-1)*4 if n even, a(n) = a(n-1)+1 if n odd.

a(2n) = (7*4^n-4)/3 = A083597(n).

a(2n+1) = (7*4^n-1)/3 = A206374(n).

a(n) = 5*a(n-2) - 4*a(n-4) with a(0)=1, a(1)=2, a(2)=8, a(3)=9.