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A115135
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+617)^2 = y^2.
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6
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0, 108, 1407, 1851, 2407, 9768, 12340, 15568, 58435, 73423, 92235, 342076, 429432, 539076, 1995255, 2504403, 3143455, 11630688, 14598220, 18322888, 67790107, 85086151, 106795107, 395111188, 495919920, 622448988, 2302878255, 2890434603
(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+617, y).
Corresponding values y of solutions (x, y) are in A160176.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (633+100*sqrt(2))/617 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (755667+461578*sqrt(2))/617^2 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)+1234 for n > 6; a(1)=0, a(2)=108, a(3)=1407, a(4)=1851, a(5)=2407, a(6)=9768.
G.f.: x*(108+1299*x+444*x^2-92*x^3-433*x^4-92*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 617*A001652(k) for k >= 0.
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PROG
| (PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1234*n+380689), print1(n, ", ")))}
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CROSSREFS
| Cf. A160176, A001652, A111258, A156035 (decimal expansion of 3+2*sqrt(2)), A160177 (decimal expansion of (633+100*sqrt(2))/617), A160178 (decimal expansion of (755667+461578*sqrt(2))/617^2).
Sequence in context: A202484 A096953 A187302 * A202309 A202427 A063809
Adjacent sequences: A115132 A115133 A115134 * A115136 A115137 A115138
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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 two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
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