

A051291


Whitney number of level n of the lattice of the ideals of the fence of order 2 n + 1.


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
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OFFSET

0,2


COMMENTS

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, 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), 163177.


LINKS

Table of n, a(n) for n=0..28.


FORMULA

G.f.: function = (1+2*t^2t^3(1t)*sqrt(12*tt^22*t^3+t^4))/(2*t*sqrt(12*tt^22*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 * A178178 A257553 A143013
Adjacent sequences: A051288 A051289 A051290 * A051292 A051293 A051294


KEYWORD

nonn


AUTHOR

Emanuele Munarini


STATUS

approved



