# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a129208 Showing 1-1 of 1 %I A129208 #10 May 28 2018 11:37:10 %S A129208 1,2,41,1562,3344161,-7118599318,654686219104361, %T A129208 -128615821825334210638,249850594047271558364480641, %U A129208 -1935878334514951131830244285524398,160443526614433014168714029147613242401001 %N A129208 Third sequence in solution to congruent number 5 problem. %C A129208 Let W(n)=A129206(n), X(n)=A129207(n), Y(n)=A129208(n), Z(n)=A129209(n). %C A129208 These four sequences correspond to the four Jacobi theta functions or Weierstrass sigma functions. %D A129208 J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, 1939. See p. 427. %H A129208 Seiichi Manyama, Table of n, a(n) for n = 0..49 %F A129208 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 A129208 Y(2*n) = Y(n)^4 + 25 * W(n)^4. %F A129208 a(n+2) * a(n-2) = -144*a(n+1) * a(n-1) + 2257 * a(n)^2. a(-n) = a(n). %o A129208 (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) ))}; %K A129208 sign %O A129208 0,2 %A A129208 _Michael Somos_, Apr 03 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE