A248205 Indices of centered octagonal numbers (A016754) that are also pentagonal numbers (A000326).

1, 50, 4851, 475300, 46574501, 4563825750, 447208348951, 43821854371400, 4294094520048201, 420777441110352250, 41231895134294472251, 4040304945719747928300, 395908652785401002501101, 38795007668023578497179550, 3801514842813525291721094751

Offset: 1

Author

Colin Barker, Jan 11 2015

Keywords

• nonn
• easy

Comments

Positive integers y in the solutions to 3*x^2 - 8*y^2 - x + 8*y - 2 = 0, the corresponding values of x being A046172.

Examples

			50 is in the sequence because the 50th centered octagonal number is 9801, which is also the 81st pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..503
• Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Crossrefs

Cf. A000290, A000326, A046172, A036353.

Programs

Magma

I:=[1,50,4851]; [n le 3 select I[n] else 99*Self(n-1)-99*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 13 2015

Mathematica

LinearRecurrence[{99, -99, 1}, {1, 50, 4851}, 20] (* Vincenzo Librandi, Jun 13 2015 *)

PARI

Vec(x*(49*x-1)/((x-1)*(x^2-98*x+1)) + O(x^100))

Formula

a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3).

G.f.: x*(49*x-1) / ((x-1)*(x^2 - 98*x + 1)).

a(n) = (1/2+1/48*(49+20*sqrt(6))^(-n)*(-12-5*sqrt(6)+(-12+5*sqrt(6))*(49+20*sqrt(6))^(2*n))). - Colin Barker, Mar 03 2016