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A253411 Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891). 3
1, 76, 646, 108871, 930811, 156991186, 1342228096, 226381180621, 1935491982901, 326441505463576, 2790978097114426, 470728424497295251, 4024588480547018671, 678790061683594287646, 5803453797970703808436, 978814798219318465489561, 8368576352085274344745321 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)