This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056932 #31 Jan 13 2025 11:09:42
%S A056932 1,20,168,887,3490,11196,30900,75966,170379,354640,693836,1288365,
%T A056932 2287844,3908776,6456600,10352796,16167765,24660252,36824128,53943395,
%U A056932 77656326,110029700,153644140,211691610,288086175,387589176,515950020,680063833,888147272
%N A056932 Antichains (or order ideals) in the poset 2*2*2*n or size of the distributive lattice J(2*2*2*n).
%C A056932 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
%D A056932 J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
%D A056932 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.
%D A056932 R. P. Stanley, Enumerative Combinatorics, Volume I, Second Edition, page 256, Proposition 3.5.1.
%H A056932 T. D. Noe, <a href="/A056932/b056932.txt">Table of n, a(n) for n = 0..1000</a>
%H A056932 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 A056932 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.
%H A056932 Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 9.
%H A056932 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%H A056932 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A056932 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).
%F A056932 G.f.: (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^9. [Berman and Koehler]
%t A056932 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 *)
%Y A056932 Cf. A000372, A006360, A006361, A006362, A056933, A056934, A056935, A056936, A056937.
%K A056932 nonn,easy
%O A056932 0,2
%A A056932 _Mitch Harris_