A253675 Centered triangular numbers (A005448) which are also centered octagonal numbers (A016754).

1, 361, 6241, 3463321, 59923081, 33254804881, 575381414521, 319312633001041, 5524812282304561, 3066039868821187801, 53049246959306977201, 29440114501108412261161, 509378863778453312776441, 282683976373603105710477121, 4891055796951461749972406281

Offset: 1

Author

Colin Barker, Jan 08 2015

Keywords

• nonn
• easy

Examples

			361 is in the sequence because it is the 16th centered triangular number and the 10th centered octagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..503
• Index entries for linear recurrences with constant coefficients, signature (1,9602,-9602,-1,1).

Crossrefs

Cf. A005448, A016754, A253673, A253674.

Programs

Mathematica

LinearRecurrence[{1,9602,-9602,-1,1},{1,361,6241,3463321,59923081},20] (* Harvey P. Dale, Dec 09 2017 *)

PARI

Vec(-x*(x^4+360*x^3-3722*x^2+360*x+1)/((x-1)*(x^2-98*x+1)*(x^2+98*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+9602*a(n-2)-9602*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+360*x^3-3722*x^2+360*x+1) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).