A225685 Number of words of length n over {0,1,2,3,4,5} which have no factor iji with i>j.

1, 6, 36, 201, 1116, 6211, 34581, 192501, 1071546, 5964820, 33203659, 184830438, 1028870637, 5727277021, 31881272165, 177469235044, 987894361908, 5499180045361, 30611553610680, 170401260906615, 948550017451201, 5280167123920333, 29392403504900866, 163614780272069160, 910772619152263675, 5069876709305861450, 28221807844318492913

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14. See Th. 3.12.

Formula

The g.f. can be written as either

1/(1-x*(1+1/(1+x^2)+1/(1+2*x^2)+1/(1+3*x^2)+1/(1+4*x^2)+1/(1+5*x^2)))

or

-(1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)*(1+5*x^2)/(-1-15*x^2-85*x^4-225*x^6-274*x^8-120*x^10+6*x+120*x^11+548*x^9+675*x^7+340*x^5+75*x^3)

Maple

F312:=proc(k) local j, t1;
t1:=add(1/(1+j*x^2), j=0..k-1);
1/(1-x*t1);
end;
seriestolist(series(F312(6), x, 40));

Mathematica

CoefficientList[1/(1 - x*Sum[1/(1 + j*x^2), {j, 0, 5}]) + O[x]^30, x] (* Jean-François Alcover, Nov 24 2017 *)

Crossrefs

Cf. A005251, A123892, A123893, A123894.

Sequence in context: A000551 A038157 A267468 * A377197 A006812 A111989

Adjacent sequences: A225682 A225683 A225684 * A225686 A225687 A225688

Keyword

nonn

Author

N. J. A. Sloane, May 21 2013

Status

approved