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

1,2

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).

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)).

Example

481 is in the sequence because it is the 13th octagonal number and the 16th centered square number.

Mathematica

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

Prog

(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))

Crossrefs

Cf. A000567, A001844, A253673, A254895.

Sequence in context: A020271 A290338 A365657 * A165384 A365688 A165376

Adjacent sequences: A254893 A254894 A254895 * A254897 A254898 A254899

Keyword

nonn,easy

Author

Colin Barker, Feb 10 2015

Status

approved