A152730 a(n) + a(n+1) + a(n+2) = n^5, with a(1) = a(2) = 0.

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

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

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 * A361700 A090027 A164784

Adjacent sequences: A152727 A152728 A152729 * A152731 A152732 A152733

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Status

approved