login
A254896
Octagonal numbers (A000567) that are also centered square numbers (A001844).
3
1, 481, 8321, 4617761, 79897441, 44339739841, 767175219361, 425750177334721, 7366416376406081, 4088053158428250401, 70732329279075969601, 39253486001477883014881, 679171818371271083701921, 376911968498137474280636161, 6521407729268615666629875041
OFFSET
1,2
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 10 2015
STATUS
approved