A006326 Total preorders. (Formerly M3931)

1, 5, 24, 122, 680, 4155, 27776, 202084, 1592064, 13513825, 123025408, 1196165886, 12374422528, 135740585015, 1573990072320, 19239037403528, 247255523459072, 3333340694137725, 47039231504678912, 693488743931379010, 10661950808321949696, 170659875799127955955

Offset

3,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=3..24.

G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30.

G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)

Maple

# After Alois P. Heinz in A000111:
b := proc(u, o) option remember;
`if`(u + o = 0, 1, add(b(o - 1 + j, u - j), j = 1..u)) end:
a := n -> (n-2)*b(n-1, 1)/2: seq(a(n), n = 3..23); # Peter Luschny, Oct 27 2017

Mathematica

b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[o-1+j, u-j], {j, 1, u}]];
a[n_] := (n-2) b[n-1, 1]/2;
Array[a, 22, 3] (* Jean-François Alcover, Jun 01 2019, from Maple *)

Crossrefs

Cf. A000111, A079502.

Sequence in context: A255715 A163610 A055825 * A058120 A271544 A275267

Adjacent sequences: A006323 A006324 A006325 * A006327 A006328 A006329

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 12 2017

Status

approved