A056782 Number of 3-element proper antichains (i.e., antichains such that every two members have nonempty intersection) on an unlabeled n-element set.

0, 0, 0, 1, 5, 18, 53, 135, 305, 633, 1220, 2217, 3834, 6359, 10172, 15776, 23807, 35075, 50585, 71576, 99551, 136332, 184084, 245384, 323260, 421256, 543484, 694709, 880393, 1106798, 1381049, 1711231, 2106469, 2577049, 3134488, 3791677, 4562974, 5464339, 6513448

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Aug 18 2000

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Vladeta Jovovic, Illustration of initial terms
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,2,4,3,-12,3,4,2,-2,-4,4,-1).

Crossrefs

Cf. A001206, A047707, A051303 (labeled case), A055484, A055485, A056005.

Programs

PARI

seq(n)=Vec((1 + x + 2*x^2 + 3*x^3 + 3*x^4 - x^5 - 3*x^7)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2) + O(x^(n-2)), -(n+1)) \\ Andrew Howroyd, Feb 02 2024

Formula

G.f.: x^3*(1 + x + 2*x^2 + 3*x^3 + 3*x^4 - x^5 - 3*x^7)/((1 - x)^8*(1 + x)^2*(1 + x + x^2)^2). - Andrew Howroyd, Feb 02 2024

Extensions

a(8) onwards from Andrew Howroyd, Feb 02 2024