A253922 Indices of centered pentagonal numbers (A005891) which are also octagonal numbers (A000567).

1, 56, 297, 26752, 142913, 12894168, 68883529, 6214961984, 33201717825, 2995598781880, 16003159107881, 1443872397903936, 7713489488280577, 695943500190915032, 3717885930192129993, 335443323219623141248, 1792013304863118375809, 161682985848358163166264

Offset: 1

Author

Colin Barker, Jan 19 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of x being A253921.

Examples

			56 is in the sequence because the 56th centered pentagonal is 7701, which is also the number 51st octagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..745
• Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

Crossrefs

Cf. A000567, A005891, A253921, A253923.

Programs

Magma

I:=[1,56,297,26752,142913]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

Mathematica

CoefficientList[Series[(55 x^3 + 241 x^2 - 55 x - 1)/((x - 1)(x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)

PARI

Vec(x*(55*x^3+241*x^2-55*x-1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(55*x^3+241*x^2-55*x-1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).