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A257714 Pentagonal numbers (A000326) that are the sum of five consecutive pentagonal numbers. 5
44290, 487065, 97731740, 1074935965, 476036316661270, 5235848584389645, 1050611935177517000, 11555515453364758825, 5117369992623387417086890, 56285147779473003009380865, 11294033255019751129047408500, 124221295646279547914265231925 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)