A259402 Pentagonal numbers (A000326) that are the sum of seven consecutive pentagonal numbers.

287, 532, 17145051, 32963672, 1106094475927, 2126616990876, 71358579001465427, 137196568515066592, 4603627364594444737551, 8851099419054387781412, 296998415728087428795555787, 571019827783678204813603176, 19160555787678205016722039960967

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..416

Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).

Formula

G.f.: -7*x*(1968*x^4+1813*x^3-195857*x^2+35*x+41) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).

Example

287 is in the sequence because P(14) = 287 = 5+12+22+35+51+70+92 = P(2)+ ... +P(8).

Mathematica

LinearRecurrence[{1, 64514, -64514, -1, 1}, {287, 532, 17145051, 32963672, 1106094475927}, 20] (* Harvey P. Dale, May 13 2022 *)

Prog

(PARI) Vec(-7*x*(1968*x^4+1813*x^3-195857*x^2+35*x+41)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^20))

Crossrefs

Cf. A000326, A133301, A257714, A257715, A259403, A259404.

Sequence in context: A295447 A203049 A306788 * A157997 A063362 A159949

Adjacent sequences: A259399 A259400 A259401 * A259403 A259404 A259405

Keyword

nonn,easy

Author

Colin Barker, Jun 26 2015

Status

approved