A207077 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2 + (x+497)^2 = y^2.

0, 91, 216, 355, 387, 528, 568, 795, 1120, 1491, 1960, 2635, 3408, 3588, 4387, 4615, 5916, 7791, 9940, 12663, 16588, 21087, 22135, 26788, 28116, 35695, 46620, 59143, 75012, 97887, 124108, 130216, 157335, 165075, 209248, 272923, 345912, 438403, 571728, 724555

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, 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).

Formula

G.f.: x^2*(77*x^17 +75*x^16 +61*x^15 +12*x^14 +47*x^13 +12*x^12 +61*x^11 +75*x^10 +77*x^9 -371*x^8 -325*x^7 -227*x^6 -40*x^5 -141*x^4 -32*x^3 -139*x^2 -125*x -91)/((x -1)*(x^18 -6*x^9 +1)). - Colin Barker, Aug 05 2012

Mathematica

LinearRecurrence[ {1, 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {0, 91, 216, 355, 387, 528, 568, 795, 1120, 1491, 1960, 2635, 3408, 3588, 4387, 4615, 5916, 7791, 9940}, 50]

Crossrefs

Cf. A207059, A207060, A207061, A207075, A207076.

Sequence in context: A305761 A339523 A260064 * A293648 A225909 A051973

Adjacent sequences: A207074 A207075 A207076 * A207078 A207079 A207080

Keyword

nonn,easy,changed

Author

Vladimir Joseph Stephan Orlovsky, Feb 14 2012

Status

approved