A253579 -id:A253579 - cp's OEIS frontend

A253410 Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).

1, 96, 817, 137712, 1177393, 198579888, 1697799169, 286352060064, 2448225223585, 412919472031680, 3530339074609681, 595429592317621776, 5090746497361935697, 858609059202538568592, 7340852918856836664673, 1238113667940468298287168, 10585504818245061108522049

Offset: 1

Colin Barker, Dec 31 2014

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.

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

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).

Cf. A005891, A016754, A253411, A253579.

LinearRecurrence[{1,1442,-1442,-1,1},{1,96,817,137712,1177393},20] (* Harvey P. Dale, Jul 12 2021 *)

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))

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)).

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

Original entry on oeis.org

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

Offset: 1

Colin Barker, Dec 31 2014

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.

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

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).

Cf. A005891, A016754, A253410, A253579.

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

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))

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)).

cp's OEIS Frontend

A253410 Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).

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