OFFSET
0,5
COMMENTS
Uniform used in the sense of Retakh, Serconek and Wilson. We use Stanley's definition of graded poset: all maximal chains have the same length n (which also implies all maximal elements have maximal rank.)
REFERENCES
R. 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 (8,-21,20,-5).
FORMULA
MATHEMATICA
Join[{0, 0}, LinearRecurrence[{8, -21, 20, -5}, {0, 1, 5, 22}, 40]]
PROG
(Python)
def a(n, d={0:0, 1:0, 2:0, 3:1, 4:5, 5:22}):
if n in d:
return d[n]
d[n]=8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4)
return d[n]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Nacin, Mar 01 2012
STATUS
approved