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%I #10 May 28 2018 11:37:02
%S 1,1,-49,-4799,4728001,18618840001,-767067390499249,
%T -54213419267800732799,250137278774864229623059201,
%U -1127677799839642474480271473583999,-195577262542844878506138849501555847171249
%N Second sequence in solution to congruent number 5 problem.
%C Let W(n)=A129206(n), X(n)=A129207(n), Y(n)=A129208(n), Z(n)=A129209(n).
%C These four sequences correspond to the four Jacobi theta functions or Weierstrass sigma functions.
%D J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, 1939. See p. 427.
%H Seiichi Manyama, <a href="/A129207/b129207.txt">Table of n, a(n) for n = 0..49</a>
%F 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.
%F X(2*n) = X(n)^4 - 50 * W(n)^4.
%F a(n+2) * a(n-2) = 144 * a(n+1) * a(n-1) + 2257 * a(n)^2. a(-n) = a(n).
%o (PARI) {a(n) = n=abs(n); if( n<1, 1, if( n<4, [1, -49, -4799][n], (144 * a(n-1) * a(n-3) + 2257 * a(n-2)^2 ) / a(n-4) ))};
%K sign
%O 0,3
%A _Michael Somos_, Apr 03 2007
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