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Search: id:A129209
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| A129209 |
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Fourth sequence in solution to congruent number 5 problem. |
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+0
4
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| 1, 3, 31, 5283, -113279, 21166249443, -518493692732129, 189797666150873887683, -249563579992463717493803519, 2960896329211804542556804051252803, -115038188620995226180802686473825513089249
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OFFSET
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0,2
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COMMENT
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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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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.
Z(2*n)= Z(n)^4 -50* 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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PROGRAM
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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: A066976 A048562 A022499 this_sequence A134721 A002707 A005042
Adjacent sequences: A129206 A129207 A129208 this_sequence A129210 A129211 A129212
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 03 2007, Apr 17 2007
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