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

0,5

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).

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

Prog

(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

Crossrefs

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

Sequence in context: A006479 A127983 A226903 * A178684 A353689 A271771

Adjacent sequences: A056779 A056780 A056781 * A056783 A056784 A056785

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda, Aug 18 2000

Extensions

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

Status

approved