A253673 Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).

1, 16, 65, 1520, 6321, 148896, 619345, 14590240, 60689441, 1429694576, 5946945825, 140095478160, 582740001361, 13727927165056, 57102573187505, 1345196766697280, 5595469432374081, 131815555209168336, 548298901799472385, 12916579213731799600

Offset: 1

Author

Colin Barker, Jan 08 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of y being A253674.

Also indices of centered square numbers (A001844) that are also octagonal numbers (A000567). - Colin Barker, Feb 10 2015

Examples

			16 is in the sequence because the 16th centered triangular number is 361, which is also the 10th centered octagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Crossrefs

Cf. A005448, A016754, A253674, A253675.

Cf. A000567, A001844, A254895, A254896.

Programs

Mathematica

LinearRecurrence[{1,98,-98,-1,1},{1,16,65,1520,6321},20] (* Harvey P. Dale, Aug 07 2023 *)

PARI

Vec(x*(3*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(3*x-1)*(5*x^2+18*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).