A129208 Third sequence in solution to congruent number 5 problem.

1, 2, 41, 1562, 3344161, -7118599318, 654686219104361, -128615821825334210638, 249850594047271558364480641, -1935878334514951131830244285524398, 160443526614433014168714029147613242401001

Offset

0,2

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.

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).

Prog

(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) ))};

Crossrefs

Sequence in context: A058246 A176941 A240553 * A133298 A054742 A113634

Adjacent sequences: A129205 A129206 A129207 * A129209 A129210 A129211

Keyword

sign

Author

Michael Somos, Apr 03 2007

Status

approved