A166753 Partial sums of A166752.

1, 2, 5, 6, 17, 18, 61, 62, 233, 234, 917, 918, 3649, 3650, 14573, 14574, 58265, 58266, 233029, 233030, 932081, 932082, 3728285, 3728286, 14913097, 14913098, 59652341, 59652342, 238609313, 238609314, 954437197, 954437198, 3817748729, 3817748730

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-4,4).

Formula

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

a(n) = a(n+1) + 5*a(n+2) - 5*a(n-3) - 4*a(n-4) + 4*a(n-5).

a(n) = (4/3)*A061547(n+1) - (1/3)*A166754(n).

a(n) = (4/3)*A061547(n+1) - (1/3)*A000975(n) + (4/3)*A011377(n-2).

Mathematica

LinearRecurrence[{1, 5, -5, -4, 4}, {1, 2, 5, 6, 17}, 40] (* G. C. Greubel, May 24 2016 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))) \\ G. C. Greubel, Sep 30 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)) )); // G. C. Greubel, Jun 06 2019
(Sage) ((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019

Crossrefs

Sequence in context: A227623 A146477 A348439 * A319756 A202854 A274911

Adjacent sequences: A166750 A166751 A166752 * A166754 A166755 A166756

Keyword

easy,nonn

Author

Paul Barry, Oct 21 2009

Status

approved