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Search: id:A161482
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| A161482 |
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+151)^2 = y^2. |
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+0
4
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| 0, 96, 189, 453, 969, 1496, 3020, 6020, 9089, 17969, 35453, 53340, 105096, 207000, 311253, 612909, 1206849, 1814480, 3572660, 7034396, 10575929, 20823353, 40999829, 61641396, 121367760, 238964880, 359272749, 707383509, 1392789753
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Corresponding values y of solutions (x, y) are in A161483.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (187+78*sqrt(2))/151 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (24723+6758*sqrt(2))/151^2 for n mod 3 = 0.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+302 for n > 6; a(1)=0, a(2)=96, a(3)=189, a(4)=453, a(5)=969, a(6)=1496.
G.f.: x*(96+93*x+264*x^2-60*x^3-31*x^4-60*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 151*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+302*n+22801), print1(n, ", ")))}
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CROSSREFS
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Cf. A161483, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A161484 (decimal expansion of (187+78*sqrt(2))/151), A161485 (decimal expansion of (24723+6758*sqrt(2))/151^2).
Sequence in context: A039600 A143847 A090762 this_sequence A044428 A044809 A115437
Adjacent sequences: A161479 A161480 A161481 this_sequence A161483 A161484 A161485
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 13 2009
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