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A253410 Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754). 4
1, 96, 817, 137712, 1177393, 198579888, 1697799169, 286352060064, 2448225223585, 412919472031680, 3530339074609681, 595429592317621776, 5090746497361935697, 858609059202538568592, 7340852918856836664673, 1238113667940468298287168, 10585504818245061108522049 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 5*x^2 - 8*y^2 - 5*x + 8*y = 0, the corresponding values of y being A253411.

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*(95*x^3 + 721*x^2 - 95*x - 1) / ((x-1)*(x^2 - 38*x + 1)*(x^2 + 38*x + 1)).

EXAMPLE

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

PROG

(PARI) Vec(x*(95*x^3+721*x^2-95*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

CROSSREFS

Cf. A005891, A016754, A253411, A253579.

Sequence in context: A187610 A269215 A096783 * A326576 A202890 A173615

Adjacent sequences:  A253407 A253408 A253409 * A253411 A253412 A253413

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Dec 31 2014

STATUS

approved

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Last modified August 7 22:44 EDT 2020. Contains 336279 sequences. (Running on oeis4.)