|
Search: id:A051291
|
|
|
| A051291 |
|
Whitney number of level n of the lattice of the ideals of the fence of order 2 n + 1. |
|
+0
3
|
|
| 1, 2, 3, 7, 17, 40, 97, 238, 587, 1458, 3640, 9124, 22951, 57904, 146461, 371281, 943045, 2399460, 6114555, 15603339, 39866932, 101976512, 261117378, 669239402, 1716737267, 4407306170, 11323050897, 29110603423, 74888578067
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
This is the second kind of Whitney numbers, which count elements, not to be confused with the first kind, which sum Mobius functions. - Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), May 07 2008
|
|
REFERENCES
|
E. Munarini, N. Zagaglia Salvi, On the Rank Polynomial of the Lattice of Order Ideals of Fences and Crowns, Discrete Mathematics 259 (2002), 163-177.
|
|
FORMULA
|
G.f.: function = (1+2*t^2-t^3-(1-t)*sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*sqrt(1-2*t-t^2-2*t^3+t^4))
|
|
EXAMPLE
|
a(2) = 3 because the ideals of size 2 of the fence F(5) = { x1 < x2 > x3 < x4 > x5 } are x1x2, x1x3, x2x3.
|
|
CROSSREFS
|
Cf. A051286, A051292.
Sequence in context: A105554 A145230 A135364 this_sequence A143013 A113483 A059801
Adjacent sequences: A051288 A051289 A051290 this_sequence A051292 A051293 A051294
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emanuele Munarini (munarini(AT)mate.polimi.it)
|
|
|
Search completed in 0.002 seconds
|
