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A006363 Number of antichains (or order ideals) in the poset B_4 X [n]; or size of the distributive lattice J(B_4 X [n]).

%I A006363 M5408 #26 Jan 22 2021 10:40:14
%S A006363 1,168,7581,160948,2068224,18561984,127234008,706987164,3320153661,
%T A006363 13583619496,49530070161,163806121656,498180781144,1408758106368,
%U A006363 3737505070344,9372218674824,22351423903953,50960797533096,111574385244253,235475590500876,480631725411720,951504952784320,1831615165328400,3435931869872580
%N A006363 Number of antichains (or order ideals) in the poset B_4 X [n]; or size of the distributive lattice J(B_4 X [n]).
%C A006363 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
%D A006363 J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
%D A006363 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006363 R. P. Stanley, Enumerative Combinatorics, Volume I, Second Edition, page 256, Proposition 3.5.1.
%H A006363 J. Berman and P. Koehler, <a href="/A006356/a006356.pdf">Cardinalities of finite distributive lattices</a>, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
%H A006363 G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1976__53__5_0">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30.
%t A006363 p = Subsets[Range[4]];
%t A006363 f[list1_, list2_] := If[ContainsAll[list2, list1], 1, 0]; \[Zeta] = Table[Table[f[p[[i]], p[[j]]], {j, 1, 16}], {i, 1, 16}]; JB4 =
%t A006363 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[
%t A006363 Table[{k, MatrixPower[\[Zeta]JB4, k][[1, 168]]}, {k, 1, 17}],n]]; Table[\[CapitalOmega][n], {n, 1, 30}] (* _Geoffrey Critzer_, Jan 15 2021 *)
%Y A006363 Cf. A056932, A002415.
%K A006363 nonn
%O A006363 0,2
%A A006363 _N. J. A. Sloane_
%E A006363 Title corrected by _Geoffrey Critzer_, Jan 15 2021
%E A006363 a(11)-a(23) from _Geoffrey Critzer_, Jan 15 2021