A166752 Interleave A007583 and A000012.

1, 1, 3, 1, 11, 1, 43, 1, 171, 1, 683, 1, 2731, 1, 10923, 1, 43691, 1, 174763, 1, 699051, 1, 2796203, 1, 11184811, 1, 44739243, 1, 178956971, 1, 715827883, 1, 2863311531, 1, 11453246123, 1, 45812984491, 1, 183251937963, 1, 733007751851, 1

Offset: 0

Author

Paul Barry, Oct 21 2009

Keywords

• easy
• nonn

Comments

Partial sums are A166753.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

Programs

Magma

[(4*4^Floor(n/2)-1)/3 - 2*Floor(2^n/3): n in [0..25]]; // G. C. Greubel, Oct 10 2017

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {1, 1, 3, 1}, 100] (* G. C. Greubel, May 24 2016 *)

PARI

x='x+O('x^50); Vec((1+x-2*x^2-4*x^3)/(1-5*x^2+4*x^4)) \\ G. C. Greubel, Oct 10 2017

Formula

G.f.: (1+x-2*x^2-4*x^3)/(1-5*x^2+4*x^4).

G.f.: (1+x)/(1-5*x^2+4*x^4) - 2*x^2*(1+2*x)/(1-5*x^2+4*x^4).

a(n) = (4*4^floor(n/2)-1)/3 - 2*floor(2^n/3).

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

a(n) = A002450(floor(n/2)+1) - 2*A000975(n-1).