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

Author

Colin Barker, Jun 26 2015

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

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

Programs

Mathematica

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

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))

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)).