A253823 Octagonal numbers (A000567) which are also centered triangular numbers (A005448).

1, 97921, 1039585, 130402572385, 1384429704481, 173658931280825761, 1843664419471976641, 231264030011583194717761, 2455233718711319470593985, 307977546462671843639087352385, 3269669116478082433043125969441, 410138010309759307549971991199125921

Offset: 1

Author

Colin Barker, Jan 14 2015

Keywords

• nonn
• easy

Examples

			97921 is in the sequence because it is the 181st octagonal number and the 256th centered triangular number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..327
• Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).

Crossrefs

Cf. A000567, A005448, A253821, A253822.

Programs

Mathematica

LinearRecurrence[{1,1331714,-1331714,-1,1},{1,97921,1039585,130402572385,1384429704481},20] (* Harvey P. Dale, Jan 22 2025 *)

PARI

Vec(-x*(x^4+97920*x^3-390050*x^2+97920*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+97920*x^3-390050*x^2+97920*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).