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A099373 Twice Chebyshev's polynomials of the first kind, T(n,x), evaluated at 83/2. 2
2, 83, 6887, 571538, 47430767, 3936182123, 326655685442, 27108485709563, 2249677658208287, 186696137145578258, 15493529705424787127, 1285776269413111753283, 106703936831582850735362 (list; graph; refs; listen; history; internal format)
OFFSET

0,1

COMMENTS

Used in A099372.

LINKS

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

FORMULA

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.

CROSSREFS

Sequence in context: A175449 A171399 A065591 * A169601 A205643 A157063

Adjacent sequences:  A099370 A099371 A099372 * A099374 A099375 A099376

KEYWORD

nonn,easy

AUTHOR

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

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Last modified February 16 17:48 EST 2012. Contains 205939 sequences.