OFFSET
0,4
COMMENTS
Here, the term uniform is used in the sense of Retakh, Serconek and Wilson. Graded is used in terms of Stanley's definition that all maximal chains have the same length n.
REFERENCES
Richard P. Stanley, Enumerative combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
V. Retakh, S. Serconek and R. Wilson, Hilbert Series of Algebras Associated to Directed Graphs and Order Homology, arXiv:1010.6295 [math.RA], 2010-2011.
Wikipedia, Graded poset
Index entries for linear recurrences with constant coefficients, signature (9,-27,30,-9).
FORMULA
MATHEMATICA
Join[{0}, LinearRecurrence[{9, -27, 30, -9}, {0, 0, 3, 24}, 40]]
PROG
(Python)
def a(n, adict={0:0, 1:0, 2:0, 3:3, 4:24}):
if n in adict:
return adict[n]
adict[n]=9*a(n-1)-27*a(n-2)+30*a(n-3)-9*a(n-4)
return adict[n]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 13 2012
STATUS
approved