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A056932 Antichains (or order ideals) in the poset 2*2*2*n or size of the distributive lattice J(2*2*2*n). 13

%I

%S 1,20,168,887,3490,11196,30900,75966,170379,354640,693836,1288365,

%T 2287844,3908776,6456600,10352796,16167765,24660252,36824128,53943395,

%U 77656326,110029700,153644140,211691610,288086175,387589176,515950020,680063833,888147272

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

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

%D 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 G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.

%H T. D. Noe, <a href="/A056932/b056932.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>

%H <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 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]

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

%K nonn,easy

%O 0,2

%A _Mitch Harris_

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Last modified February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)