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A118676
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+79)^2 = y^2.
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9
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0, 20, 161, 237, 341, 1140, 1580, 2184, 6837, 9401, 12921, 40040, 54984, 75500, 233561, 320661, 440237, 1361484, 1869140, 2566080, 7935501, 10894337, 14956401, 46251680, 63497040, 87172484, 269574737, 370088061, 508078661, 1571196900, 2157031484, 2961299640
(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+79, y).
Corresponding values y of solutions (x, y) are in A159758.
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) = (83+18*sqrt(2))/79 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (10659+6110*sqrt(2))/79^2 for n mod 3 = 0.
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FORMULA
| a(n) = 6*a(n-3)-a(n-6)+158 for n > 6; a(1)=0, a(2)=20, a(3)=161, a(4)=237, a(5)=341, a(6)=1140.
G.f.: x*(20+141*x+76*x^2-16*x^3-47*x^4-16*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 79*A001652(k) for k >= 0.
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MATHEMATICA
| LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 20, 161, 237, 341, 1140, 1580}, 75] (* From Vladimir Joseph Stephan Orlovsky, Feb 07 2012 *)
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PROG
| (PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+158*n+6241), print1(n, ", ")))}
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CROSSREFS
| Cf. A159758, A028871, A118337, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159759 (decimal expansion of (83+18*sqrt(2))/79), A159760 (decimal expansion of (10659+6110*sqrt(2))/79^2).
Sequence in context: A059601 A125357 A126515 * A067534 A041768 A056114
Adjacent sequences: A118673 A118674 A118675 * A118677 A118678 A118679
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KEYWORD
| nonn,changed
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AUTHOR
| Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 19 2006
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009
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