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

0,3

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).

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).

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A360121 A339175 A134761 * A205483 A230262 A323854

Adjacent sequences: A166749 A166750 A166751 * A166753 A166754 A166755

Keyword

easy,nonn

Author

Paul Barry, Oct 21 2009

Status

approved