OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of y being A253922.
LINKS
Colin Barker, Table of n, a(n) for n = 1..745
Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).
FORMULA
a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+50*x^3-262*x^2+50*x+1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).
EXAMPLE
51 is in the sequence because the 51st octagonal number is 7701, which is also the 56th centered pentagonal number.
MATHEMATICA
CoefficientList[Series[(x^4 + 50 x^3 - 262 x^2 + 50 x + 1)/((1 - x) (x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)
PROG
(PARI) Vec(-x*(x^4+50*x^3-262*x^2+50*x+1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))
(Magma) I:=[1, 51, 271, 24421, 130461]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 19 2015
STATUS
approved