OFFSET
0,2
COMMENTS
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
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.
R. P. Stanley, Enumerative Combinatorics, Volume I, Second Edition, page 256, Proposition 3.5.1.
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]
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 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
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved