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A227139 Chebyshev S-polynomial evaluated at x = 48. 0
1, 48, 2303, 110496, 5301505, 254361744, 12204062207, 585540624192, 28093745899009, 1347914262528240, 64671790855456511, 3102898046799384288, 148874434455514989313, 7142869955817920102736, 342708883444804649942015 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence, with a(-1) = 0, appears in the solution of the Pell equation u^2 - 23*v^2 = +1 for the solutions v = 5*a(n), n >= -1, together with u = A114051(n+1).

LINKS

Table of n, a(n) for n=0..14.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (48,-1).

FORMULA

a(n) = S(n, 48), with the Chebyshev S-polynomial, with coefficients given in A049310.

a(n) = 48*a(n-1) - a(n-2), n >= 1, a(-1) = 0, a(0) = 1.

O.g.f.: 1/(1 - 48*x + x^2).

a(n) = A174767(n+2)/5, n >= 0.

MATHEMATICA

LinearRecurrence[{48, -1}, {1, 48}, 20] (* Harvey P. Dale, Aug 26 2013 *)

CROSSREFS

Cf. A049310, A114051, A174767.

Sequence in context: A218750 A263504 A158783 * A009992 A042105 A206046

Adjacent sequences:  A227136 A227137 A227138 * A227140 A227141 A227142

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 02 2013

STATUS

approved

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Last modified December 10 09:49 EST 2018. Contains 318047 sequences. (Running on oeis4.)