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A208737 Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with no 3-element antichain. 2
0, 0, 0, 1, 7, 37, 175, 778, 3325, 13837, 56524, 227866, 909832, 3607294, 14227447, 55894252, 218937532, 855650749, 3338323915, 13007422705, 50631143323, 196928737582, 765495534433, 2974251390529, 11552064922624, 44856304154086 (list; graph; refs; listen; history; text; internal format)
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 (10,-36,57,-39,9).

FORMULA

a(n) = 10*a(n-1) - 36*a(n-2) + 57*a(n-3) - 39*a(n-4) + 9*a(n-5), a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 7, a(5) = 37.

G.f: (x^3 - 3*x^4 + 3*x^5)/(1 - 10*x + 36*x^2 - 57*x^3 + 39*x^4 - 9*x^5); (x^3*(1 - 3*x + 3*x^2)) / ((1 - x) (1 - 3*x) (1 - 6*x + 9*x^2 - 3*x^3)).

a(n) = A124292(n) - A124302(n).

MATHEMATICA

Join[{0}, LinearRecurrence[{10, -36, 57, -39, 9}, {0, 0, 1, 7, 37}, 40]]

PROG

(Python)

def a(n, d={0:0, 1:0, 2:0, 3:1, 4:7, 5:37}):

    if n in d:

        return d[n]

    d[n]=10*a(n-1) - 36*a(n-2) + 57*a(n-3) - 39*a(n-4) + 9*a(n-5)

    return d[n]

CROSSREFS

Cf. A208736, A206901, A206902, A206947-A206950, A001906, A025192, A081567, A124302, A124292, A088305, A086405, A012781.

Sequence in context: A169726 A305781 A172063 * A005061 A099454 A177414

Adjacent sequences:  A208734 A208735 A208736 * A208738 A208739 A208740

KEYWORD

nonn,easy

AUTHOR

David Nacin, Mar 01 2012

STATUS

approved

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Last modified August 1 07:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)