A089927 Expansion of 1/((1-x^2)(1-5x+x^2)).

1, 5, 25, 120, 576, 2760, 13225, 63365, 303601, 1454640, 6969600, 33393360, 159997201, 766592645, 3672966025, 17598237480, 84318221376, 403992869400, 1935646125625, 9274237758725, 44435542668001, 212903475581280

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (5,0,-5,1).

Formula

a(n) = 5*a(n-1) - 5*a(n-3) + a(n-4).

a(n) = ((5-sqrt(21))^n*(23 - 5*sqrt(21)) + (5 + sqrt(21))^n*(23 + 5*sqrt(21)))/42/2^n + (-1)^n/14 - 1/6. [corrected by Jason Yuen, Aug 25 2024]

a(n) = Sum_{k=0..floor(n/2)} U(n-2k, 5/2) where U is the Chebyshev polynomial of the second kind.

a(n) = (-1)^n/14 - 1/6 + (23*A004254(n+1) - 5*A004254(n))/21. - R. J. Mathar, Mar 22 2011

Mathematica

CoefficientList[Series[1/((1-x^2)(1-5x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 0, -5, 1}, {1, 5, 25, 120}, 30] (* Harvey P. Dale, Apr 12 2015 *)

Crossrefs

Cf. A003690, A003769.

Sequence in context: A269405 A269674 A269602 * A269463 A068539 A123871

Adjacent sequences: A089924 A089925 A089926 * A089928 A089929 A089930

Keyword

easy,nonn

Author

Paul Barry, Nov 15 2003

Status

approved