0,2

Used for all positive integer solutions of Pell equation x^2 - 629*y^2 = -4. See A098261 with A098262.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)= S(n, 627)=U(n, 627/2)= S(2*n+1, sqrt(629))/sqrt(629) 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)=627*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=627; a(-1):=0.

a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (627+25*sqrt(629))/2 and am := (627-25*sqrt(629))/2 = 1/ap.

G.f.: 1/(1-627*x+x^2).

Sequence in context: A031523 A129974 A031703 this_sequence A098261 A110904 A058832

Adjacent sequences: A098257 A098258 A098259 this_sequence A098261 A098262 A098263

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 10 2004