OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1060,0,0,0,-1).
FORMULA
a(n) = 1060*a(n-4)-a(n-8).
G.f.: -59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1).
EXAMPLE
413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI) Vec(-59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1) + O(x^100))
(Magma) I:=[413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727]; [n le 8 select I[n] else 1060*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 10 2015
STATUS
approved