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Search: id:A118675
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| A118675 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+47)^2 = y^2. |
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+0
9
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| 0, 16, 85, 141, 225, 616, 940, 1428, 3705, 5593, 8437, 21708, 32712, 49288, 126637, 190773, 287385, 738208, 1112020, 1675116, 4302705, 6481441, 9763405, 25078116, 37776720, 56905408, 146166085, 220178973, 331669137, 851918488, 1283297212
(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+47, y).
Corresponding values y of solutions (x, y) are in A159750.
For the generic case x^2+(x+p)^2 = y^2 with p = m^2-2 a (prime) number > 7 in A028871, see A118337.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (51+14*sqrt(2))/47 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (3267+1702*sqrt(2))/47^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+94 for n > 6; a(1)=0, a(2)=16, a(3)=85, a(4)=141, a(5)=225, a(6)=616.
G.f.: x*(16+69*x+56*x^2-12*x^3-23*x^4-12*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 47*A001652(k) for k >= 0.
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PROGRAM
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(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+94+2209), print1(n, ", ")))}
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CROSSREFS
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Cf. A159750, A028871, A118337, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159751 (decimal expansion of (51+14*sqrt(2))/47), A159752 (decimal expansion of (3267+1702*sqrt(2))/47^2).
Sequence in context: A151502 A030693 A159501 this_sequence A070052 A022676 A035291
Adjacent sequences: A118672 A118673 A118674 this_sequence A118676 A118677 A118678
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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 19 2006
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EXTENSIONS
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Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009
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