A205672 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+329)^2 = y^2.

0, 87, 112, 184, 235, 376, 451, 595, 660, 987, 1440, 1575, 1971, 2256, 3055, 3484, 4312, 4687, 6580, 9211, 9996, 12300, 13959, 18612, 21111, 25935, 28120, 39151, 54484, 59059, 72487, 82156, 109275, 123840, 151956, 164691, 228984, 318351, 345016, 423280

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A185394, A198294, A203619, A204765, A205644, A206426.

Programs

Mathematica

LinearRecurrence[ {1,0,0,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,-1,1}, {0,87,112,184,235,376,451,595,660,987,1440,1575,1971,2256,3055,3484,4312,4687,6580}, 120]

Formula

G.f.: x^2*(69*x^17 +15*x^16 +36*x^15 +21*x^14 +47*x^13 +21*x^12 +36*x^11 +15*x^10 +69*x^9 -327*x^8 -65*x^7 -144*x^6 -75*x^5 -141*x^4 -51*x^3 -72*x^2 -25*x -87)/((x-1)*(x^18 -6*x^9 +1)). - Colin Barker, Aug 05 2012