A227139 Chebyshev S-polynomial evaluated at x = 48.

1, 48, 2303, 110496, 5301505, 254361744, 12204062207, 585540624192, 28093745899009, 1347914262528240, 64671790855456511, 3102898046799384288, 148874434455514989313, 7142869955817920102736, 342708883444804649942015

Offset: 0

Author

Wolfdieter Lang, Jul 02 2013

Keywords

• nonn
• easy

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

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (48,-1).

Crossrefs

Cf. A049310, A114051, A174767.

Programs

Mathematica

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

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.