A123889 Expansion of g.f.: x/((1-x^2)^4 -1+x).

1, 4, 16, 58, 208, 740, 2628, 9327, 33096, 117432, 416668, 1478400, 5245576, 18612052, 66038209, 234312956, 831375680, 2949839102, 10466448480, 37136447100, 131765393560, 467522347871, 1658835752336, 5885785066224, 20883602126968, 74097989119616

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. Burstein and T. Mansour, Words restricted by 3-letter ..., arXiv:math/0112281 [math.CO], 2001.

A. Burstein and T. Mansour, Words Restricted by 3-Letter Generalized Multipermutation Patterns, Annals. Combin., 7 (2003), 1-14.

Index entries for linear recurrences with constant coefficients, signature (4,0,-6,0,4,0,-1).

Maple

seq(coeff(series(1/(1-4*x+6*x^3-4*x^5+x^7), x, n+1), x, n), n = 0 .. 30); # G. C. Greubel, Aug 07 2019

Mathematica

CoefficientList[Series[x/((1-x^2)^4 -1+x), {x, 0, 30}], x] (* G. C. Greubel, Aug 07 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(x/((1-x^2)^4 -1+x)) \\ G. C. Greubel, Aug 07 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x/((1-x^2)^4 -1+x) )); // G. C. Greubel, Aug 07 2019
(Sage)
def A123889_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x/((1-x^2)^4 -1+x) ).list()
A123889_list(30) # G. C. Greubel, Aug 07 2019
(GAP) a:=[1, 4, 16, 58, 208, 740, 2628];; for n in [8..30] do a[n]:=4*a[n-1] -6*a[n-3] +4*a[n-5]-a[n-7]; od; a; # G. C. Greubel, Aug 07 2019

Crossrefs

Sequence in context: A092688 A267466 A255299 * A180143 A224128 A123893

Adjacent sequences: A123886 A123887 A123888 * A123890 A123891 A123892

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2006

Status

approved