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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

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

LINKS

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]

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).

FORMULA

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]

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A281204 A186259 A292281 * A304508 A010826 A022712

Adjacent sequences:  A056929 A056930 A056931 * A056933 A056934 A056935

KEYWORD

nonn,easy

AUTHOR

Mitch Harris

STATUS

approved

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Last modified October 20 10:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)