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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. MATHEMATICA LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 96, 817, 137712, 1177393}, 20] (* Harvey P. Dale, Jul 12 2021 *) 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 May 26 03:59 EDT 2024. Contains 372807 sequences. (Running on oeis4.)