A253674 Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448).

1, 10, 40, 931, 3871, 91180, 379270, 8934661, 37164541, 875505550, 3641745700, 85790609191, 356853914011, 8406604195120, 34968041827330, 823761420512521, 3426511245164281, 80720212606031890, 335763133984272160, 7909757073970612651, 32901360619213507351

Offset: 1

Author

Colin Barker, Jan 08 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of x being A253673.

Examples

			10 is in the sequence because the 10th centered octagonal number is 361, which is also the 16th centered triangular 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, A253673, A253675.

Programs

Mathematica

LinearRecurrence[{1,98,-98,-1,1},{1,10,40,931,3871},30] (* Harvey P. Dale, Oct 01 2015 *)

PARI

Vec(-x*(x^2-5*x+1)*(x^2+14*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*(x^2-5*x+1)*(x^2+14*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).