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A129208
Third sequence in solution to congruent number 5 problem.
4
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
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
KEYWORD
sign
AUTHOR
Michael Somos, Apr 03 2007
STATUS
approved