A006361 -id:A006361 - cp's OEIS frontend

A056932 Antichains (or order ideals) in the poset 222n or size of the distributive lattice J(222n).

1, 20, 168, 887, 3490, 11196, 30900, 75966, 170379, 354640, 693836, 1288365, 2287844, 3908776, 6456600, 10352796, 16167765, 24660252, 36824128, 53943395, 77656326, 110029700, 153644140, 211691610, 288086175, 387589176, 515950020, 680063833, 888147272

Offset: 0

Mitch Harris

a(n) is the number of order preserving maps from B_3 into [n+1]. a(n) is also the number of length n+1 multichains from bottom to top in J(B_3). See Stanley reference for bijections with description in title. - Geoffrey Critzer, Jan 07 2021

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials, Applicable Algebra in Engineering, Communication and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.
R. P. Stanley, Enumerative Combinatorics, Volume I, Second Edition, page 256, Proposition 3.5.1.

T. D. Noe, Table of n, a(n) for n = 0..1000
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.
Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 9.
Index entries for sequences related to posets
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A000372, A006360, A006361, A006362, A056933, A056934, A056935, A056936, A056937.

Table[48*Binomial[n+8,8] - 96*Binomial[n+7,7] + 63*Binomial[n+6,6] - 15*Binomial[n+5,5] + Binomial[n+4,4], {n, 0, nn}] (* T. D. Noe, May 29 2012 *)

a(n) = 48*C(n+8, 8) - 96*C(n+7, 7) + 63*C(n+6, 6) - 15*C(n+5, 5) + C(n+4, 4).

G.f.: (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^9. [Berman and Koehler]

A006360 Antichains (or order ideals) in the poset 223n or size of the distributive lattice J(223n).

Original entry on oeis.org

1, 50, 887, 8790, 59542, 307960, 1301610, 4701698, 14975675, 43025762, 113414717, 277904900, 639562508, 1393844960, 2896063220, 5768600412, 11066514565, 20526933442, 36936277875, 64660182026, 110394412610

Offset: 0

N. J. A. Sloane

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials, Applicable Algebra in Engineering, Communication and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.
Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 9.
Index entries for sequences related to posets.

Cf. A000217, A000330, A050446, A050447, A006356, A006357, A006358, A006359, A000372, A056932, A006361, A006362, A056933, A056934, A056935, A056936, A056937.

Empirical G.f.: (x+1)*(x^6+36*x^5+279*x^4+594*x^3+279*x^2+36*x+1)/(1-x)^13. - Colin Barker, May 29 2012

More terms from Mitch Harris, Jul 16 2000

A006362 Antichains (or order ideals) in the poset 225n or size of the distributive lattice J(225n).

Original entry on oeis.org

1, 196, 11196, 307960, 5157098, 60112692, 530962446, 3764727340, 22326282261, 114158490576, 515063238810, 2087929609236, 7714649716552, 26285397502428, 83379798088110, 248202756212336, 697998155989501, 1864955619299196

Offset: 0

N. J. A. Sloane

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).

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.
Index entries for sequences related to posets.

Cf. A000372, A056932, A006360, A006361, A056933, A056934, A056935, A056936, A056937.

More terms from Mitch Harris, Jul 16 2000

A056933 Antichains (or order ideals) in the poset 226n or size of the distributive lattice J(226n).

Original entry on oeis.org

1, 336, 30900, 1301610, 32046856, 530962446, 6479344016, 61951251333, 485198553532, 3217462615688, 18528857431906, 94529315562186, 434088353496446, 1817613939845670, 7014049051387480, 25167786776727516

Offset: 0

Mitch Harris

Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
Index entries for sequences related to posets

Cf. A000372, A006360, A006361, A006362, A056932, A056934, A056935, A056936, A056937.

A056934 Antichains (or order ideals) in the poset 227n or size of the distributive lattice J(227n).

Original entry on oeis.org

1, 540, 75966, 4701698, 164489084, 3764727340, 61951251333, 782318812002, 7946895019096, 67270102239520, 487605585591870, 3092040981805272, 17451258588313354, 88902214572208640, 413569247116248032

Offset: 0

Mitch Harris

Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
Index entries for sequences related to posets

Cf. A000372, A006360, A006361, A006362, A056932, A056933, A056935, A056936, A056937.

A056935 Antichains (or order ideals) in the poset 233n or size of the distributive lattice J(233n).

Original entry on oeis.org

1, 175, 8790, 211250, 3092808, 31635580, 246441430, 1549486490, 8192995479, 37548347569, 152602439244, 559835910940, 1880152558980, 5846268790220, 16988036626948, 46486024648180, 120562654732065, 297976456047575

Offset: 0

Mitch Harris

Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
Index entries for sequences related to posets

Cf. A000372, A006360, A006361, A006362, A056932, A056933, A056934, A056936, A056937.

A056936 Antichains (or order ideals) in the poset 234n or size of the distributive lattice J(234n).

Original entry on oeis.org

1, 490, 59542, 3092808, 89613429, 1691136270, 22954776044, 239831111938, 2024703039198, 14318216628378, 87184226214168, 467034400160664, 2239064967256060, 9741467994941264, 38902816410160608

Offset: 0

Mitch Harris

Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
Index entries for sequences related to posets

Cf. A000372, A006360, A006361, A006362, A056932, A056933, A056934, A056935, A056937.

A056937 Number of antichains (or order ideals) in the poset 333n or size of the distributive lattice J(333n).

Original entry on oeis.org

1, 980, 211250, 17792748, 781429368, 21238316210, 398925639186, 5585711269074, 61555624183223, 555895303974238, 4242859829536322, 28038281717424550, 163544036697306396, 855242362045150398

Offset: 0

Mitch Harris

Berman and Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), p. 103-124

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]
Index entries for sequences related to posets

Cf. A000372, A006360, A006361, A006362, A056932, A056933, A056934, A056935, A056936.

cp's OEIS Frontend

A056932 Antichains (or order ideals) in the poset 2*2*2*n or size of the distributive lattice J(2*2*2*n).

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A006360 Antichains (or order ideals) in the poset 2*2*3*n or size of the distributive lattice J(2*2*3*n).

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A006362 Antichains (or order ideals) in the poset 2*2*5*n or size of the distributive lattice J(2*2*5*n).

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A056933 Antichains (or order ideals) in the poset 2*2*6*n or size of the distributive lattice J(2*2*6*n).

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A056934 Antichains (or order ideals) in the poset 2*2*7*n or size of the distributive lattice J(2*2*7*n).

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A056935 Antichains (or order ideals) in the poset 2*3*3*n or size of the distributive lattice J(2*3*3*n).

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A056936 Antichains (or order ideals) in the poset 2*3*4*n or size of the distributive lattice J(2*3*4*n).

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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).

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A056932 Antichains (or order ideals) in the poset 222n or size of the distributive lattice J(222n).

A006360 Antichains (or order ideals) in the poset 223n or size of the distributive lattice J(223n).

A006362 Antichains (or order ideals) in the poset 225n or size of the distributive lattice J(225n).

A056933 Antichains (or order ideals) in the poset 226n or size of the distributive lattice J(226n).

A056934 Antichains (or order ideals) in the poset 227n or size of the distributive lattice J(227n).

A056935 Antichains (or order ideals) in the poset 233n or size of the distributive lattice J(233n).

A056936 Antichains (or order ideals) in the poset 234n or size of the distributive lattice J(234n).

A056937 Number of antichains (or order ideals) in the poset 333n or size of the distributive lattice J(333n).