A208737
Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with no 3-element antichain.
Original entry on oeis.org
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
Offset: 0
- R. Stanley, Enumerative combinatorics. Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100.
- 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).
Cf.
A208736,
A206901,
A206902,
A206947-
A206950,
A001906,
A025192,
A081567,
A124302,
A124292,
A088305,
A086405,
A012781.
-
Join[{0}, LinearRecurrence[{10, -36, 57, -39, 9}, {0, 0, 1, 7, 37}, 40]]
-
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]
A122935
Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 6, 1, 0, 1, 10, 19, 10, 1, 0, 1, 15, 45, 45, 15, 1, 0, 1, 21, 90, 141, 90, 21, 1, 0, 1, 28, 161, 357, 357, 161, 28, 1, 0, 1, 36, 266, 784, 1107, 784, 266, 36, 1, 0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1, 0, 1, 55, 615, 2850, 6765, 8953
Offset: 0
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 3, 1;
0, 1, 6, 6, 1;
0, 1, 10, 19, 10, 1;
0, 1, 15, 45, 45, 15, 1;
0, 1, 21, 90, 141, 90, 21, 1;
0, 1, 28, 161, 357, 357, 161, 28, 1;
0, 1, 36, 266, 784, 1107, 784, 255, 36, 1;
0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1;
0, 1, 55, 615, 2850, 6765, 8953, 6765, 2850, 615, 55, 1;
A198793
Triangle T(n,k), read by rows, given by (1,0,0,1,0,0,0,0,0,0,0,...) DELTA (0,1,1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 16, 8, 0, 1, 5, 20, 40, 40, 16, 0, 1, 6, 30, 80, 120, 96, 32, 0, 1, 7, 42, 140, 280, 336, 224, 64, 0, 1, 8, 56, 224, 560, 896, 896, 512, 128, 0, 1, 9, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 0
Offset: 0
Triangle begins :
1
1, 0
1, 1, 0
1, 2, 2, 0
1, 3, 6, 4, 0
1, 4, 12, 16, 8, 0,
1, 5, 20, 40, 40, 16, 0
Comments