A123892 Expansion of g.f.: (1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4-2*x^5).

1, 3, 9, 24, 63, 167, 444, 1179, 3129, 8306, 22051, 58539, 155400, 412535, 1095149, 2907266, 7717839, 20488343, 54389880, 144387411, 383301505, 1017540554, 2701238539, 7170907923, 19036423288, 50535499231, 134155279397, 356138541458, 945431750839, 2509813152639

Offset

0,2

Comments

a(n) = number of words of length n over {0,1,2} which do not contain a factor jkj with j>k. - N. J. A. Sloane, May 21 2013

Links

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

A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, arXiv:math/0112281 [math.CO], 2001; Annals. Combin., 7 (2003), 1-14.

Index entries for linear recurrences with constant coefficients, signature (3,-3,6,-2,2).

Formula

G.f. can be written 1/(1-x*(1+1/(1+x^2)+1/(1+2*x^2))). - N. J. A. Sloane, May 21 2013

Maple

seq(coeff(series((1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4-2*x^5), x, n+1), x, n), n = 0..30); # G. C. Greubel, Aug 06 2019

Mathematica

LinearRecurrence[{3, -3, 6, -2, 2}, {1, 3, 9, 24, 63}, 30] (* Jean-François Alcover, Jan 09 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4 -2*x^5)) \\ G. C. Greubel, Aug 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4-2*x^5)) )); // G. C. Greubel, Aug 06 2019
(Sage) ((1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4-2*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 06 2019
(GAP) a:=[1, 3, 9, 24, 63];; for n in [6..30] do a[n]:=3*a[n-1]-3*a[n-2] +6*a[n-3]-2*a[n-4]+2*a[n-5]; od; a; # G. C. Greubel, Aug 06 2019

Crossrefs

Cf. A005251, A123893, A123894, A225685.

Sequence in context: A123888 A166290 A097134 * A269531 A064831 A153582

Adjacent sequences: A123889 A123890 A123891 * A123893 A123894 A123895

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2006

Status

approved