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Search: id:A129640
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| A129640 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+313)^2 = y^2. |
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+0
5
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| 0, 155, 464, 939, 1764, 3515, 6260, 11055, 21252, 37247, 65192, 124623, 217848, 380723, 727112, 1270467, 2219772, 4238675, 7405580, 12938535, 24705564, 43163639, 75412064, 143995335, 251576880, 439534475, 839267072, 1466298267
(list; graph; listen)
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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+313, y).
Corresponding values y of solutions (x, y) are in A160574.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (363+130*sqrt(2))/313 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (119187+47998*sqrt(2))/313^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+626 for n > 6; a(1)=0, a(2)=155, a(3)=464, a(4)=939, a(5)=1764, a(6)=3515.
G.f.: x*(155+309*x+475*x^2-105*x^3-103*x^4-105*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 313*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+626*n+97969), print1(n, ", ")))}
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CROSSREFS
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Cf. A160574, A001652, A129298, A156035 (decimal expansion of 3+2*sqrt(2)), A160575 (decimal expansion of (363+130*sqrt(2))/313), A160576 (decimal expansion of (119187+47998*sqrt(2))/313^2).
Sequence in context: A119609 A063340 A105986 this_sequence A028382 A131960 A101535
Adjacent sequences: A129637 A129638 A129639 this_sequence A129641 A129642 A129643
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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 31 2007
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EXTENSIONS
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Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 08 2009
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