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A161486
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Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+191)^2 = y^2.
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4
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0, 69, 336, 573, 936, 2449, 3820, 5929, 14740, 22729, 35020, 86373, 132936, 204573, 503880, 775269, 1192800, 2937289, 4519060, 6952609, 17120236, 26339473, 40523236, 99784509, 153518160, 236187189, 581587200, 894769869, 1376600280
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OFFSET
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1,2
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COMMENTS
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Corresponding values y of solutions (x, y) are in A161487.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (209+60*sqrt(2))/191 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (52323+26522*sqrt(2))/191^2 for n mod 3 = 0.
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LINKS
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Table of n, a(n) for n=1..29.
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FORMULA
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a(n) = 6*a(n-3)-a(n-6)+382 for n > 6; a(1)=0, a(2)=69, a(3)=336, a(4)=573, a(5)=936, a(6)=2449.
G.f.: x*(69+267*x+237*x^2-51*x^3-89*x^4-51*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 191*A001652(k) for k >= 0.
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MATHEMATICA
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Transpose[NestList[Flatten[{Rest[#], 6#[[4]]-First[#]+382}]&, {0, 69, 336, 573, 936, 2449}, 40]][[1]] (* From Harvey P. Dale, Apr 01 2011 *)
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PROG
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(PARI) {forstep(n=0, 10000000, [1, 3], if(issquare(2*n^2+382*n+36481), print1(n, ", ")))}
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CROSSREFS
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Cf. A161487, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A161488 (decimal expansion of (209+60*sqrt(2))/191), A161489 (decimal expansion of (52323+26522*sqrt(2))/191^2).
Sequence in context: A158732 A069216 A158736 * A211692 A113707 A093269
Adjacent sequences: A161483 A161484 A161485 * A161487 A161488 A161489
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Jun 13 2009
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STATUS
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approved
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