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A122694
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+761)^2 = y^2.
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4
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0, 583, 820, 2283, 5440, 6783, 15220, 33579, 41400, 90559, 197556, 243139, 529656, 1153279, 1418956, 3088899, 6723640, 8272119, 18005260, 39190083, 48215280, 104944183, 228418380, 281021083, 611661360, 1331321719, 1637912740
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also values x of Pythagorean triples (x, x+761, y).
Corresponding values y of solutions (x, y) are in A160200.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2) = A156035.
lim_{n -> infinity} a(n)/a(n-1) = (1003+462*sqrt(2))/761 = A160201 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (591603+85478*sqrt(2))/761^2 = A160202 for n mod 3 = 0.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).
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FORMULA
| a(n) = 6*a(n-3)-a(n-6)+1522 for n > 6; a(1)=0, a(2)=583, a(3)=820, a(4)=2283, a(5)=5440, a(6)=6783.
G.f.: x*(583+237*x+1463*x^2-341*x^3-79*x^4-341*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 761*A001652(k) for k >= 0.
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PROG
| (PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1522*n+579121), print1(n, ", ")))}
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CROSSREFS
| Cf. A160200, A001652, A115135.
Sequence in context: A172883 A162705 A059468 * A032373 A205069 A187050
Adjacent sequences: A122691 A122692 A122693 * A122695 A122696 A122697
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KEYWORD
| nonn,easy
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 03 2007
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EXTENSIONS
| Edited and one term added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
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