OFFSET
0,2
COMMENTS
a(n) is the number of order preserving maps from B_4 into [n+1]. a(n) is also the number of length n+1 multichains from bottom to top in J(B_4). See Stanley reference for bijections with description in title. - Geoffrey Critzer, Jan 15 2021
REFERENCES
J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Volume I, Second Edition, page 256, Proposition 3.5.1.
LINKS
J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30.
MATHEMATICA
p = Subsets[Range[4]];
f[list1_, list2_] := If[ContainsAll[list2, list1], 1, 0]; \[Zeta] = Table[Table[f[p[[i]], p[[j]]], {j, 1, 16}], {i, 1, 16}]; JB4 =
Complement[Subsets[Range[16]], Level[Table[Select[Subsets[Range[16]], MemberQ[#, i] && !ContainsAll[Level[Position[\[Zeta][[All, i]], 1], {2}]][#] &], {i, 2, 16}], {2}] // DeleteDuplicates]; \[Zeta]JB4 =Table[Table[f[JB4[[i]], JB4[[j]]], {j, 1, 168}], {i, 1, 168}]; \[CapitalOmega][n_] := Expand[InterpolatingPolynomial[
Table[{k, MatrixPower[\[Zeta]JB4, k][[1, 168]]}, {k, 1, 17}], n]]; Table[\[CapitalOmega][n], {n, 1, 30}] (* Geoffrey Critzer, Jan 15 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Title corrected by Geoffrey Critzer, Jan 15 2021
a(11)-a(23) from Geoffrey Critzer, Jan 15 2021
STATUS
approved