A258132 Octagonal numbers (A000567) that are the sum of fifteen consecutive octagonal numbers.

4715040, 8463840, 1122749669280, 2015496399840, 267373851637578960, 479974343542849680, 63672943775553479639280, 114302050117965712710960, 15163202176330482896520455040, 27220118818712616412771202880, 3610995292612020914167620625112640

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..370

Index entries for linear recurrences with constant coefficients, signature (1,238142,-238142,-1,1).

Formula

G.f.: -240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)).

Example

4715040 is in the sequence because Oct(1254) = 4715040 = 300833 + 302736 + 304645 + 306560 + 308481 + 310408 + 312341 + 314280 + 316225 + 318176 + 320133 + 322096 + 324065 + 326040 + 328021 = Oct(317) + ... + Oct(331).

Mathematica

CoefficientList[Series[-240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 18 2017 *)

Prog

(PARI) Vec(-240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)) + O('x^20))

Crossrefs

Cf. A000567, A258128, A258129, A258130, A258131.

Sequence in context: A069340 A205942 A271142 * A083641 A224641 A323310

Adjacent sequences: A258129 A258130 A258131 * A258133 A258134 A258135

Keyword

nonn,easy

Author

Colin Barker, May 21 2015

Status

approved