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Search: id:A129289
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| A129289 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+73)^2 = y^2. |
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+0
8
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| 0, 44, 95, 219, 455, 744, 1460, 2832, 4515, 8687, 16683, 26492, 50808, 97412, 154583, 296307, 567935, 901152, 1727180, 3310344, 5252475, 10066919, 19294275, 30613844, 58674480, 112455452, 178430735, 341980107, 655438583, 1039970712
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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+73, y).
Corresponding values y of solutions (x, y) are in A160041.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (89+36*sqrt(2))/73 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (5907+1802*sqrt(2))/73^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+146 for n > 6; a(1)=0, a(2)=44, a(3)=95, a(4)=219, a(5)=455, a(6)=744.
G.f.: x*(44+51*x+124*x^2-28*x^3-17*x^4-28*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 73*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 100000000, [3 , 1], if(issquare(2*n^2+146*n+5329), print1(n, ", ")))}
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CROSSREFS
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Cf. A160041, A129288, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A160042 (decimal expansion of (89+36*sqrt(2))/73), A160043 (decimal expansion of (5907+1802*sqrt(2))/73^2).
Sequence in context: A118087 A044182 A044563 this_sequence A039527 A050944 A118483
Adjacent sequences: A129286 A129287 A129288 this_sequence A129290 A129291 A129292
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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), May 26 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 04 2009
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