0,1

Used in A099372.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)=83*a(n-1)-a(n-2), n >= 1; a(-1)=83, a(0)=2.

a(n) = S(n, 83) - S(n-2, 83) = 2*T(n, 83/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 83)= A097839(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, case. See A049310 and A053120.

G.f.: (2-83*x)/(1-83*x+x^2).

a(n) = ap^n + am^n, with ap := (83+9*sqrt(85))/2 and am := (83-9*sqrt(85))/2.

Sequence in context: A007353 A108312 A065591 this_sequence A078166 A101578 A041881

Adjacent sequences: A099370 A099371 A099372 this_sequence A099374 A099375 A099376

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004