A254896 Octagonal numbers (A000567) that are also centered square numbers (A001844).

1, 481, 8321, 4617761, 79897441, 44339739841, 767175219361, 425750177334721, 7366416376406081, 4088053158428250401, 70732329279075969601, 39253486001477883014881, 679171818371271083701921, 376911968498137474280636161, 6521407729268615666629875041

Offset: 1

Author

Colin Barker, Feb 10 2015

Keywords

• nonn
• easy

Examples

			481 is in the sequence because it is the 13th octagonal number and the 16th centered square 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. A000567, A001844, A253673, A254895.

Programs

Mathematica

LinearRecurrence[{1,9602,-9602,-1,1},{1,481,8321,4617761,79897441},30] (* Harvey P. Dale, Feb 04 2017 *)

PARI

Vec(-x*(x^4+480*x^3-1762*x^2+480*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+480*x^3-1762*x^2+480*x+1) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).