A051291 Whitney number of level n of the lattice of the ideals of the fence of order 2 n + 1.

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

Offset: 0

Author

Emanuele Munarini

Keywords

• nonn

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

Examples

			a(2) = 3 because the ideals of size 2 of the fence F(5) = { x1 < x2 > x3 < x4 > x5 } are x1x2, x1x3, x2x3.
		

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.

Crossrefs

Cf. A051286, A051292.

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))