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

1,2

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.

Links

Colin Barker, Table of n, a(n) for n = 1..503

Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000290, A000326, A046172, A036353.

Sequence in context: A047683 A010564 A183689 * A174756 A231937 A230477

Adjacent sequences: A248202 A248203 A248204 * A248206 A248207 A248208

Keyword

nonn,easy

Author

Colin Barker, Jan 11 2015

Status

approved