A253411 -id:A253411 - 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)).

A253579 Centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).

Original entry on oeis.org

1, 22801, 1666681, 47411143081, 3465632747641, 98584929298781641, 7206305041398228481, 204993755756525779060081, 14984516863488437537571601, 426256225957302372068628976801, 31158234954289838149958560780201, 886340998518823181233611960679431001

Offset: 1

Colin Barker, Jan 04 2015

			22801 is in the sequence because it is the 96th centered pentagonal number and the 76th centered octagonal number.

Colin Barker, Table of n, a(n) for n = 1..317
Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1).

Cf. A005891, A016754, A253410, A253411.

Vec(-x*(x^4+22800*x^3-435482*x^2+22800*x+1)/((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)) + O(x^100))

a(n) = a(n-1)+2079362*a(n-2)-2079362*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+22800*x^3-435482*x^2+22800*x+1) / ((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula