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A152730 a(n) + a(n+1) + a(n+2) = n^5, with a(1) = a(2) = 0. 4
0, 0, 1, 31, 211, 782, 2132, 4862, 9813, 18093, 31143, 50764, 79144, 118924, 173225, 245675, 340475, 462426, 616956, 810186, 1048957, 1340857, 1694287, 2118488, 2623568, 3220568, 3921489, 4739319, 5688099, 6782950, 8040100, 9476950 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (5,-10,11,-10,11,-10,5,-1).

FORMULA

a(n) = (1/3)*(n^5 - 5*n^4 + (10/3)*n^3 + 10*n^2 - 5*n - (13/3)) + ((13/54)*i)*sqrt(3)*((-1/2 - (1/2)*i*sqrt(3))^n - (-1/2 + (1/2)*i*sqrt(3))^n) + (13/18)*((-1/2 - (1/2)*i*sqrt(3))^n + (-1/2 + (1/2)*i*sqrt(3))^n) with n >= 0 where i = sqrt(-1). - Paolo P. Lava, Dec 23 2008

G.f.: x^3*(x^4 + 26*x^3 + 66*x^2 + 26*x + 1) / ((x-1)^6*(x^2 + x + 1)). - Colin Barker, Oct 28 2014

EXAMPLE

0 + 0 + 1 = 1^5; 0 + 1 + 31 = 2^5; 1 + 31 + 211 = 3^5; ...

MATHEMATICA

k0=k1=0; lst={k0, k1}; Do[kt=k1; k1=n^5-k1-k0; k0=kt; AppendTo[lst, k1], {n, 1, 5!}]; lst

LinearRecurrence[{5, -10, 11, -10, 11, -10, 5, -1}, {0, 0, 1, 31, 211, 782, 2132, 4862}, 50] (* G. C. Greubel, Sep 01 2018 *)

CoefficientList[Series[x^2*(x^4 + 26*x^3 + 66*x^2 + 26*x + 1) / ((x - 1)^6*(x^2 + x + 1)), {x, 0, 50}], x] (* Stefano Spezia, Sep 02 2018 *)

PROG

(PARI) concat([0, 0], Vec(x^3*(x^4+26*x^3+66*x^2+26*x+1)/((x-1)^6*(x^2+x+1)) + O(x^100))) \\ Colin Barker, Oct 28 2014

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0, 0] cat Coefficients(R!(x^3*(x^4+26*x^3+66*x^2+26*x+1)/((x-1)^6*(x^2+x+1)))); // G. C. Greubel, Sep 01 2018

CROSSREFS

Cf. A152728, A152729, A152725, A152726, A000212.

Sequence in context: A181124 A142328 A022521 * A090027 A164784 A290008

Adjacent sequences:  A152727 A152728 A152729 * A152731 A152732 A152733

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)