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A129991
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+241)^2 = y^2.
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6
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0, 23, 620, 723, 840, 4223, 4820, 5499, 25200, 28679, 32636, 147459, 167736, 190799, 860036, 978219, 1112640, 5013239, 5702060, 6485523, 29219880, 33234623, 37800980, 170306523, 193706160, 220320839, 992619740, 1129002819, 1284124536, 5785412399, 6580311236
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OFFSET
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1,2
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COMMENTS
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Also values x of Pythagorean triples (x, x+241, y).
Corresponding values y of solutions (x, y) are in A159565.
For the generic case x^2+(x+p)^2 = y^2 with p = 2*m^2-1 a (prime) number in A066436 see A118673 or A129836.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (243+22*sqrt(2))/241 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (137283+87958*sqrt(2))/241^2 for n mod 3 = 0.
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LINKS
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+482 for n > 6; a(1)=0, a(2)=23, a(3)=620, a(4)=723, a(5)=840, a(6)=4223.
G.f.: x*(23+597*x+103*x^2-21*x^3-199*x^4-21*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 241*A001652(k) for k >= 0.
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MATHEMATICA
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LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 23, 620, 723, 840, 4223, 4820}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2012 *)
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PROG
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(PARI) {forstep(n=0, 500000000, [3, 1], if(issquare(2*n^2+482*n+58081), print1(n, ", ")))}
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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