OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,6,0,0,0,0,0,-1).
FORMULA
a(n) = 6*a(n-6)-a(n-12).
G.f.: -5*x*(39*x^11 +31*x^10 +27*x^9 +23*x^8 +21*x^7 +21*x^6 -211*x^5 -159*x^4 -131*x^3 -99*x^2 -77*x -49) / ((x^6 -2*x^3 -1)*(x^6 +2*x^3 -1)).
EXAMPLE
245 is in the sequence because 245^2 = 60025 = 7^2+8^2+...+56^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1}, {245, 385, 495, 655, 795, 1055, 1365, 2205, 2855, 3795, 4615, 6135}, 50] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI) Vec(-5*x*(39*x^11 +31*x^10 +27*x^9 +23*x^8 +21*x^7 +21*x^6 -211*x^5 -159*x^4 -131*x^3 -99*x^2 -77*x -49) / ((x^6 -2*x^3 -1)*(x^6 +2*x^3 -1)) + O(x^100))
(Magma) I:=[245, 385, 495, 655, 795, 1055, 1365, 2205, 2855, 3795, 4615, 6135]; [n le 12 select I[n] else 6*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 08 2015
STATUS
approved