OFFSET
0,4
COMMENTS
We do not assume all maximal elements have maximal rank and thus use graded poset to mean: For every element x, all maximal chains among those with x as greatest element have the same finite length. Here, the term uniform used in the sense of Retakh, Serconek and Wilson.
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 (13,-59,115,-109,51,-9).
FORMULA
a(n) = 13*a(n-1) - 59*a(n-2) + 115*a(n-3) - 109*a(n-4) + 51*a(n-5) - 9*a(n-6), a(1)=0, a(2)=0, a(3)=3, a(4)=33, a(5)=259, a(6)=1762.
G.f.: (3*x^3-6*x^4+7*x^5-3*x^6)/((-1+7*x-10*x^2+3*x^3)*(-1+6*x-7*x^2+3*x^3)).
MATHEMATICA
Join[{0}, LinearRecurrence[{13, -59, 115, -109, 51, -9}, {0, 0, 3, 33, 259, 1762}, 40]]
PROG
(Python)
def a(n, adict={0:0, 1:0, 2:0, 3:3, 4:33, 5:259, 6:1762}):
if n in adict:
return adict[n]
adict[n]=13*a(n-1)-59*a(n-2)+115*a(n-3)-109*a(n-4)+51*a(n-5)-9*a(n-6)
return adict[n]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 13 2012
STATUS
approved