login
A098257
Chebyshev polynomials S(n,531).
2
1, 531, 281960, 149720229, 79501159639, 42214966048080, 22416067470370841, 11902889611800868491, 6320411967798790797880, 3356126852011546112805789, 1782097038006163187109076079, 946290171054420640808806592160
OFFSET
0,2
COMMENTS
Used for all positive integer solutions of Pell equation x^2 - 533*y^2 = -4. See A098258 with A098259.
FORMULA
a(n)= S(n, 531)=U(n, 531/2)= S(2*n+1, sqrt(533))/sqrt(533) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x).
a(n)=531*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=531; a(-1):=0.
a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (531+23*sqrt(533))/2 and am := (531-23*sqrt(533))/2 = 1/ap.
G.f.: 1/(1-531*x+x^2).
CROSSREFS
Sequence in context: A158367 A225937 A225936 * A174780 A191950 A333102
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 10 2004
STATUS
approved