A253411 Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).

1, 76, 646, 108871, 930811, 156991186, 1342228096, 226381180621, 1935491982901, 326441505463576, 2790978097114426, 470728424497295251, 4024588480547018671, 678790061683594287646, 5803453797970703808436, 978814798219318465489561, 8368576352085274344745321

Offset

1,2

Comments

Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of x being A253410.

Links

Colin Barker, Table of n, a(n) for n = 1..633

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1) + 1442*a(n-2) - 1442*a(n-3) - a(n-4) + a(n-5).

G.f.: -x*(x^4 + 75*x^3 - 872*x^2 + 75*x + 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).

Example

76 is in the sequence because the 76th centered octagonal number is 22801, which is also the 96th centered pentagonal number.

Mathematica

LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 76, 646, 108871, 930811}, 20] (* Harvey P. Dale, Feb 04 2016 *)

Prog

(PARI) Vec(-x*(x^4+75*x^3-872*x^2+75*x+1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

Crossrefs

Cf. A005891, A016754, A253410, A253579.

Sequence in context: A129626 A200167 A178262 * A185481 A007250 A137061

Adjacent sequences: A253408 A253409 A253410 * A253412 A253413 A253414

Keyword

nonn,easy

Author

Colin Barker, Dec 31 2014

Status

approved