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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 05 2015
STATUS
approved