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A129208
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Third sequence in solution to congruent number 5 problem.
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4
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1, 2, 41, 1562, 3344161, -7118599318, 654686219104361, -128615821825334210638, 249850594047271558364480641, -1935878334514951131830244285524398, 160443526614433014168714029147613242401001
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OFFSET
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0,2
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COMMENTS
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Let W(n)=A129206(n), X(n)=A129207(n), Y(n)=A129208(n), Z(n)=A129209(n).
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LINKS
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Table of n, a(n) for n=0..10.
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FORMULA
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Right triangle with sides |10*Y(n)*W(n) / (X(n)*Z(n))|, |X(n)*Z(n) / (Y(n)*W(n))|, |2*Y(2*n) / W(2*n)| has area 5.
Y(2*n) = Y(n)^4 + 25 * W(n)^4.
a(n+2) * a(n-2) = -144*a(n+1) * a(n-1) + 2257 * a(n)^2. a(-n) = a(n).
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PROG
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(PARI) {a(n) = n=abs(n); if( n<1, 1, if( n<4, [2, 41, 1562][n], (-144 * a(n-1) * a(n-3) + 2257 * a(n-2)^2 ) / a(n-4) ))}
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CROSSREFS
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Sequence in context: A112767 A058246 A176941 * A133298 A054742 A113634
Adjacent sequences: A129205 A129206 A129207 * A129209 A129210 A129211
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 03 2007
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STATUS
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approved
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