OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-66*y^2-2112*y-22880 = 0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,46,0,0,0,0,0,-1).
FORMULA
a(n) = 46*a(n-6)-a(n-12).
G.f.: -11*x*(8*x^11+5*x^10+5*x^9+8*x^8+13*x^7+23*x^6-328*x^5-127*x^4-103*x^3-40*x^2-23*x-13) / (x^12-46*x^6+1).
EXAMPLE
143 is in the sequence because 143^2 = 20449 = 7^2+8^2+...+39^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, -1}, {143, 253, 440, 1133, 1397, 3608, 6325, 11495, 20152, 52063, 64207, 165880}, 50] (* Vincenzo Librandi, May 08 2015 *)
PROG
(PARI) Vec(-11*x*(8*x^11+5*x^10+5*x^9+8*x^8+13*x^7+23*x^6-328*x^5-127*x^4-103*x^3-40*x^2-23*x-13) / (x^12-46*x^6+1) + O(x^100))
(Magma) I:=[143, 253, 440, 1133, 1397, 3608, 6325, 11495, 20152, 52063, 64207, 165880]; [n le 12 select I[n] else 46*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 07 2015
STATUS
approved