A207078 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+511)^2 = y^2.

0, 33, 156, 308, 365, 584, 665, 969, 1380, 1533, 1700, 2349, 3185, 3504, 4745, 5208, 6956, 9333, 10220, 11189, 14960, 19824, 21681, 28908, 31605, 41789, 55640, 60809, 66456, 88433, 116781, 127604, 169725, 185444, 244800, 325529, 355656, 388569, 516660

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 14 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• MathWorld, Diophantine equation
• Wikipedia, Diophantine equation
• 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. A207060, A207061, A207075, A207076, A207077.

Programs

Mathematica

LinearRecurrence[ {1, 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {0, 33, 156, 308, 365, 584, 665, 969, 1380, 1533, 1700, 2349, 3185, 3504, 4745, 5208, 6956, 9333, 10220}, 50]

Formula

G.f.: x^2*(31*x^17 +89*x^16 +76*x^15 +23*x^14 +73*x^13 +23*x^12 +76*x^11 +89*x^10 +31*x^9 -153*x^8 -411*x^7 -304*x^6 -81*x^5 -219*x^4 -57*x^3 -152*x^2 -123*x -33)/((x -1)*(x^18 -6*x^9 +1)). [Colin Barker, Aug 05 2012]

a(n) = a(n-1)+6*a(n-9)-6*a(n-10)-a(n-18)+a(n-19). - Wesley Ivan Hurt, May 31 2021