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Search: id:A123654
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| A123654 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+809)^2 = y^2. |
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+0
5
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| 0, 264, 1491, 2427, 3811, 10764, 16180, 24220, 64711, 96271, 143127, 379120, 563064, 836160, 2211627, 3283731, 4875451, 12892260, 19140940, 28418164, 75143551, 111563527, 165635151, 437970664, 650241840, 965394360, 2552682051
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OFFSET
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1,2
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COMMENT
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Also values x of Pythagorean triples (x, x+809, y).
Corresponding values y of solutions (x, y) are in A160203.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (873+232*sqrt(2))/809 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (989043+524338*sqrt(2))/809^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1618 for n > 6; a(1)=0, a(2)=264, a(3)=1491, a(4)=2427, a(5)=3811, a(6)=10764.
G.f.: x*(264+1227*x+936*x^2-200*x^3-409*x^4-200*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 809*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1618*n+654481), print1(n, ", ")))}
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CROSSREFS
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Cf. A160203, A001652, A115135, A156035 (decimal expansion of 3+2*sqrt(2)), A160204 (decimal expansion of (873+232*sqrt(2))/809), A160205 (decimal expansion of (989043+524338*sqrt(2))/809^2).
Sequence in context: A050240 A105683 A160971 this_sequence A014745 A004533 A092724
Adjacent sequences: A123651 A123652 A123653 this_sequence A123655 A123656 A123657
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KEYWORD
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nonn
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AUTHOR
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Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 03 2007
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EXTENSIONS
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Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
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