A006361 Antichains (or order ideals) in the poset 2*2*4*n or size of the distributive lattice J(2*2*4*n).

1, 105, 3490, 59542, 650644, 5157098, 32046856, 164489084, 723509159, 2801747767, 9748942554, 30967306114, 90930233726, 249319296218, 643622467414, 1575086681342, 3675063064675, 8215220917795

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

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.
• 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.

Crossrefs

Cf. A000372, A056932, A006360, A006362, A056933, A056934, A056935, A056936, A056937.

Formula

Empirical G.f.: (x^10 +88*x^9 +1841*x^8 +13812*x^7 +44050*x^6 +64374*x^5 +44050*x^4 +13812*x^3 +1841*x^2 +88*x +1)/(1-x)^17. - Colin Barker, May 29 2012

Extensions

More terms from Mitch Harris, Jul 16 2000