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Search: id:A129975
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| A129975 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+953)^2 = y^2. |
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+0
4
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| 0, 132, 2295, 2859, 3535, 15792, 19060, 22984, 94363, 113407, 136275, 552292, 663288, 796572, 3221295, 3868227, 4645063, 18777384, 22547980, 27075712, 109444915, 131421559, 157811115, 637894012, 765983280, 919792884, 3717921063
(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+953, y).
Corresponding values y of solutions (x, y) are in A160212.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (969+124*sqrt(2))/953 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (1947891+1218490*sqrt(2))/953^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+1906 for n > 6; a(1)=0, a(2)=132, a(3)=2295, a(4)=2859, a(5)=3535, a(6)=15792.
G.f.: x*(132+2163*x+564*x^2-116*x^3-721*x^4-116*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 953*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+1906*n+908209), print1(n, ", ")))}
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CROSSREFS
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Cf. A160212, A001652, A129974, A156035 (decimal expansion of 3+2*sqrt(2)), A160213 (decimal expansion of (969+124*sqrt(2))/953), A160214 (decimal expansion of (1947891+1218490*sqrt(2))/953^2).
Sequence in context: A090199 A033278 A119982 this_sequence A064303 A023902 A168180
Adjacent sequences: A129972 A129973 A129974 this_sequence A129976 A129977 A129978
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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 13 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 18 2009
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