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A166753 Partial sums of A166752. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)