login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208736 Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank level between 0 and 1. 2
0, 0, 0, 1, 5, 22, 91, 361, 1392, 5265, 19653, 72694, 267179, 977593, 3565600, 12975457, 47142021, 171075606, 620303547, 2247803785, 8141857808, 29481675889, 106728951109, 386314552438, 1398132674955, 5059626441177, 18308871648576, 66249898660801 (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 (8,-21,20,-5).

FORMULA

a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4), a(2) = 0, a(3) = 1, a(4) = 5, a(5) = 22.

G.f.: (x^3 - 3*x^4 + 3*x^5)/(1 - 8*x + 21*x^2 - 20*x^3 + 5*x^4); (x^3 * (1 - 3*x + 3*x^2))/((1 - 3*x + x^2)*(1 - 5*x + 5*x^2)) .

a(n) = A081567(n-2) - A001519(n-1).

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

Cf. A208737, A206901, A206902, A206947-A206950, A001906, A025192, A081567, A124302, A124292, A088305, A086405, A012781.

Sequence in context: A128566 A097138 A105467 * A050185 A216597 A085812

Adjacent sequences:  A208733 A208734 A208735 * A208737 A208738 A208739

KEYWORD

nonn,easy

AUTHOR

David Nacin, Mar 01 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 04:26 EST 2021. Contains 341756 sequences. (Running on oeis4.)