A258131 Octagonal numbers (A000567) that are the sum of eleven consecutive octagonal numbers.

49665, 348161, 19701781, 138502485, 7841194625, 55123576321, 3120775694421, 21939044808725, 1242060885120385, 8731684710231681, 494337111502154261, 3475188575627335765, 196744928316972210945, 1383116321414969338241, 78303987133043437737301

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..766

Index entries for linear recurrences with constant coefficients, signature (1,398,-398,-1,1).

Formula

G.f.: -11*x*(95*x^4 -64*x^3 -37550*x^2 +27136*x +4515)/((x-1)*(x^2 -20*x +1)*(x^2 +20*x +1)).

Example

49665 is in the sequence because Oct(129) = 49665 = 3400 + 3605 + 3816 + 4033 + 4256 + 4485 + 4720 + 4961 + 5208 + 5461 + 5720 = Oct(34) + ... + Oct(44).

Mathematica

CoefficientList[Series[-11*x*(95*x^4 -64*x^3 -37550*x^2 +27136*x +4515)/((x-1)*(x^2 -20*x +1)*(x^2 +20*x +1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 18 2017 *)
Select[Total/@Partition[Table[n(3n-2), {n, 5*10^6}], 11, 1], IntegerQ[(Sqrt[1+3#]+1)/3]&] (* Harvey P. Dale, Aug 31 2018 *)

Prog

(PARI) Vec(-11*x*(95*x^4 -64*x^3 -37550*x^2 +27136*x +4515)/((x-1)*(x^2 -20*x +1)*(x^2 +20*x +1)) + O('x^20))

Crossrefs

Cf. A000567, A258128, A258129, A258130, A258132.

Sequence in context: A251881 A187856 A258320 * A081636 A151636 A023944

Adjacent sequences: A258128 A258129 A258130 * A258132 A258133 A258134

Keyword

nonn,easy

Author

Colin Barker, May 21 2015

Status

approved