A185647 Expansion of (1+2x)*(1+2*x^2)/((1-x)*(1+x)*(1-2*x^2)).

1, 2, 5, 10, 13, 26, 29, 58, 61, 122, 125, 250, 253, 506, 509, 1018, 1021, 2042, 2045, 4090, 4093, 8186, 8189, 16378, 16381, 32762, 32765, 65530, 65533, 131066, 131069, 262138, 262141, 524282, 524285, 1048570, 1048573, 2097146, 2097149, 4194298, 4194301

Offset: 0

Author

Philippe Deléham, Apr 23 2013

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Crossrefs

Cf. A036563, A131130

Programs

Mathematica

LinearRecurrence[{0, 3, 0, -2}, {1, 2, 5, 10}, 50] (* G. C. Greubel, Jul 09 2017 *)

PARI

x='x+O('x^50); Vec((1+2*x)*(1+2*x^2)/((1-x)*(1+x)*(1-2*x^2))) \\ G. C. Greubel, Jul 09 2017

Formula

a(n) = a(n-1)*2 if n odd.

a(n) = a(n-1)+3 if n even.

a(2n) = 2^(n+2)-3 = A036563(n+2).

a(2n+1) = 2^(n+3)-6 = A131130(n+1).

a(n) = 3*a(n-2) - 2*a(n-4) with a(0)=1, a(1)=2, a(2)=5, a(3)=10.