A206950
Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with no 3-element antichain.
Original entry on oeis.org
0, 0, 0, 3, 33, 259, 1762, 11093, 66592, 387264, 2202053, 12314587, 67995221, 371697914, 2015659707, 10859379024, 58190011080, 310409500291, 1649579166385, 8738000970251, 46158910515154, 243260704208613, 1279386591175904, 6716811592446952, 35209193397256085
Offset: 0
- 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).
Cf.
A206949 (unique maximal element added.)
Cf.
A206947,
A206948 (requiring exactly two elements in each rank level above 0 with and without maximal element.)
-
Join[{0},LinearRecurrence[{13, -59, 115, -109, 51, -9}, {0, 0, 3, 33, 259, 1762}, 40]]
-
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]
A206947
Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank above 0.
Original entry on oeis.org
0, 0, 0, 2, 14, 70, 306, 1248, 4888, 18666, 70110, 260414, 959882, 3519232, 12854064, 46824210, 170243566, 618125238, 2242100898, 8126927456, 29442587720, 106626616954, 386046638142, 1397431266222, 5057790129274, 18304064121600, 66237312391776
Offset: 0
- R. Stanley, Enumerative combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100.
- 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).
Cf.
A206948 (removing unique maximal element.)
Cf.
A206949,
A206950 (allowing one or two elements in each rank level above 0 with and without maximal element.)
-
Join[{0}, LinearRecurrence[{8, -21, 20, -5}, {0, 0, 2, 14}, 40]]
-
def a(n,adict={0:0,1:0,2:0,3:2,4:14}):
if n in adict:
return adict[n]
adict[n]=8*a(n-1)-21*a(n-2)+20*a(n-3)-5*a(n-4)
return adict[n]
A206948
Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank level above 0.
Original entry on oeis.org
0, 0, 0, 2, 19, 131, 791, 4446, 23913, 124892, 638878, 3218559, 16027375, 79093773, 387540260, 1887974063, 9154751912, 44221373872, 212931964415, 1022594028515, 4900116587043, 23437066655010, 111923110602497
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..200
- 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 (11, -40, 55, -30, 6).
Cf.
A206947 (unique maximal element added).
Cf.
A206949,
A206950 (allowing one or two elements in each rank level above 0 with and without maximal element).
-
LinearRecurrence[{11, -40, 55, -30, 6}, {0, 0, 0, 2, 19, 131}, 23] (* David Nacin, Feb 29 2012; a(0) added by Georg Fischer, Apr 03 2019 *)
-
def a(n, adict={0:0, 1:0, 2:0, 3:2, 4:19, 5:131}):
if n in adict:
return adict[n]
adict[n]=11*a(n-1)-40*a(n-2)+55*a(n-3)-30*a(n-4)+6*a(n-5)
return adict[n]
for n in range(0,40):
print(a(n))
Showing 1-3 of 3 results.
Comments