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Search: id:A129298
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| A129298 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+89)^2 = y^2. |
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+0
9
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| 0, 51, 120, 267, 540, 931, 1780, 3367, 5644, 10591, 19840, 33111, 61944, 115851, 193200, 361251, 675444, 1126267, 2105740, 3936991, 6564580, 12273367, 22946680, 38261391, 71534640, 133743267, 223003944, 416934651, 779513100, 1299762451
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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+89, y).
Corresponding values y of solutions (x, y) are in A160055.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (107+42*sqrt(2))/89 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (8979+2990*sqrt(2))/89^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+178 with for n > 6; a(1)=0, a(2)=51, a(3)=120, a(4)=267, a(5)=540, a(6)=931.
G.f.: x*(51+69*x+147*x^2-33*x^3-23*x^4-33*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 89*A001652(k), k >= 0. (Zak Seidov, May 28, 2007)
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PROGRAM
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(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+178*n+7921), print1(n, ", ")))}
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CROSSREFS
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Cf. A160055, A129289, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A160056 (decimal expansion of (107+42*sqrt(2))/89), A160057 (decimal expansion of (8979+2990*sqrt(2))/89^2).
Sequence in context: A031894 A068564 A063314 this_sequence A065010 A116630 A097644
Adjacent sequences: A129295 A129296 A129297 this_sequence A129299 A129300 A129301
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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 26 2007
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EXTENSIONS
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Edited and three terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 04 2009
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