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A253675
Centered triangular numbers (A005448) which are also centered octagonal numbers (A016754).
3
1, 361, 6241, 3463321, 59923081, 33254804881, 575381414521, 319312633001041, 5524812282304561, 3066039868821187801, 53049246959306977201, 29440114501108412261161, 509378863778453312776441, 282683976373603105710477121, 4891055796951461749972406281
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+360*x^3-3722*x^2+360*x+1) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).
EXAMPLE
361 is in the sequence because it is the 16th centered triangular number and the 10th centered octagonal number.
MATHEMATICA
LinearRecurrence[{1, 9602, -9602, -1, 1}, {1, 361, 6241, 3463321, 59923081}, 20] (* Harvey P. Dale, Dec 09 2017 *)
PROG
(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))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 08 2015
STATUS
approved