A056936
Antichains (or order ideals) in the poset 2*3*4*n or size of the distributive lattice J(2*3*4*n).
Original entry on oeis.org
1, 490, 59542, 3092808, 89613429, 1691136270, 22954776044, 239831111938, 2024703039198, 14318216628378, 87184226214168, 467034400160664, 2239064967256060, 9741467994941264, 38902816410160608
Offset: 0
- Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124
A056937
Number of antichains (or order ideals) in the poset 3*3*3*n or size of the distributive lattice J(3*3*3*n).
Original entry on oeis.org
1, 980, 211250, 17792748, 781429368, 21238316210, 398925639186, 5585711269074, 61555624183223, 555895303974238, 4242859829536322, 28038281717424550, 163544036697306396, 855242362045150398
Offset: 0
- Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124
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]).
Original entry on oeis.org
1, 168, 7581, 160948, 2068224, 18561984, 127234008, 706987164, 3320153661, 13583619496, 49530070161, 163806121656, 498180781144, 1408758106368, 3737505070344, 9372218674824, 22351423903953, 50960797533096, 111574385244253, 235475590500876, 480631725411720, 951504952784320, 1831615165328400, 3435931869872580
Offset: 0
- 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.
-
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 *)
Comments