A257714 Pentagonal numbers (A000326) that are the sum of five consecutive pentagonal numbers.

44290, 487065, 97731740, 1074935965, 476036316661270, 5235848584389645, 1050611935177517000, 11555515453364758825, 5117369992623387417086890, 56285147779473003009380865, 11294033255019751129047408500, 124221295646279547914265231925

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..398

Index entries for linear recurrences with constant coefficients, signature (1,0,0,10749957122,-10749957122,0,0,-1,1).

Formula

G.f.: -5*x*(29*x^8 +275*x^7 +60401*x^6 +606965*x^5 -16071841615*x^4 +195440845*x^3 +19448935*x^2 +88555*x +8858) / ((x -1)*(x^2 -322*x +1)*(x^2 +322*x +1)*(x^4 +103682*x^2 +1)).

Example

44290 is in the sequence because P(172) = 44290 = 8400+8626+8855+9087+9322 = P(75)+ ... +P(79).

Mathematica

CoefficientList[Series[5 (29 x^8 + 275 x^7 + 60401 x^6 + 606965 x^5 - 16071841615 x^4 + 195440845 x^3 + 19448935 x^2 + 88555 x + 8858)/((1 - x) (x^2 - 322 x + 1) (x^2 + 322 x + 1) (x^4 + 103682 x^2 + 1)), {x, 0, 33}], x] (* Vincenzo Librandi, May 06 2015 *)

Prog

(PARI) Vec(-5*x*(29*x^8 +275*x^7 +60401*x^6 +606965*x^5 -16071841615*x^4 +195440845*x^3 +19448935*x^2 +88555*x +8858) / ((x -1)*(x^2 -322*x +1)*(x^2 +322*x +1)*(x^4 +103682*x^2 +1)) + O(x^100))

Crossrefs

Cf. A000326, A133301, A257715, A259402, A259403, A259404.

Sequence in context: A240099 A245483 A015388 * A204668 A115959 A045937

Adjacent sequences: A257711 A257712 A257713 * A257715 A257716 A257717

Keyword

nonn,easy

Author

Colin Barker, May 05 2015

Status

approved