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Search: id:A111258
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| A111258 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+601)^2 = y^2. |
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+0
5
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| 0, 539, 560, 1803, 4740, 4859, 12020, 29103, 29796, 71519, 171080, 175119, 418296, 998579, 1022120, 2439459, 5821596, 5958803, 14219660, 33932199, 34731900, 82879703, 197772800, 202433799, 483059760, 1152705803, 1179872096
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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+601, y).
Corresponding values y of solutions (x, y) are in A160098.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (843+418*sqrt(2))/601 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (361299+5950*sqrt(2))/601^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1202 for n > 6; a(1)=0, a(2)=539, a(3)=560, a(4)=1803, a(5)=4740, a(6)=4859.
G.f.: x*(539+21*x+1243*x^2-297*x^3-7*x^4-297*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 601*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+1202*n+361201), print1(n, ", ")))}
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CROSSREFS
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Cf. A160098, A001652, A101152, A156035 (decimal expansion of 3+2*sqrt(2)), A160099 (decimal expansion of (843+418*sqrt(2))/601), A160100 (decimal expansion of (361299+5950*sqrt(2))/601^2).
Sequence in context: A059949 A077076 A033916 this_sequence A118630 A146123 A159207
Adjacent sequences: A111255 A111256 A111257 this_sequence A111259 A111260 A111261
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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 one term added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
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