A129207 Second sequence in solution to congruent number 5 problem.

1, 1, -49, -4799, 4728001, 18618840001, -767067390499249, -54213419267800732799, 250137278774864229623059201, -1127677799839642474480271473583999, -195577262542844878506138849501555847171249

Offset

0,3

Comments

Let W(n)=A129206(n), X(n)=A129207(n), Y(n)=A129208(n), Z(n)=A129209(n).

These four sequences correspond to the four Jacobi theta functions or Weierstrass sigma functions.

References

J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, 1939. See p. 427.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..49

Formula

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.

X(2*n) = X(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).

Prog

(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) ))};

Crossrefs

Sequence in context: A218317 A283229 A109344 * A243944 A144928 A053772

Adjacent sequences: A129204 A129205 A129206 * A129208 A129209 A129210

Keyword

sign

Author

Michael Somos, Apr 03 2007

Status

approved