OFFSET
0,3
COMMENTS
Number of nonisomorphic graded posets with 0 and uniform hasse graph of rank n, with exactly 2 elements of each rank level above 0, for n > 0. (Uniform used in the sense of Retakh, Serconek and Wilson.) Here, 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. - David Nacin, Feb 13 2012
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.
Index entries for linear recurrences with constant coefficients, signature (5,-4,1).
FORMULA
a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n).
G.f.: x*(1-x)/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 03 2012
MATHEMATICA
LinearRecurrence[{5, -4, 1}, {0, 1, 4}, 25] (* Harvey P. Dale, Jan 10 2012 *)
PROG
(Magma) I:=[0, 1, 4 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012
(Python)
def a(n, adict={0:0, 1:1, 2:4}):
if n in adict:
return adict[n]
adict[n]=5*a(n-1) - 4*a(n-2) + a(n-3)
return adict[n] # David Nacin, Feb 27 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Initial term 0 added by Colin Barker, Feb 03 2012
STATUS
approved