A051303 Number of 3-element proper antichains of an n-element set.

0, 0, 0, 1, 30, 605, 9030, 110901, 1200150, 11932285, 111885510, 1006471301, 8786447670, 75039565965, 630534185190, 5234341175701, 43059373189590, 351805681631645, 2859550165976070, 23152657123816101, 186907026783617910, 1505512392025329325

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (29,-343,2135,-7504,14756,-14832,5760).

Formula

a(n) = (8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!.

G.f.: x^3*(360*x^3-78*x^2-x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Nov 27 2012

a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7) for n > 6. - Wesley Ivan Hurt, Oct 06 2017

E.g.f.: exp(x)*(exp(x) - 1)^3*(2 - 2*exp(x) - 3*exp(2*x) + 3*exp(3*x) + exp(4*x))/6. - Stefano Spezia, Sep 28 2024

Maple

A051303:=n->(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: seq(A051303(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017

Mathematica

Table[(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!, {n, 0, 25}] (* G. C. Greubel, Oct 06 2017 *)

Prog

(PARI) for(n=0, 25, print1((8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2 )/3!, ", ")) \\ G. C. Greubel, Oct 06 2017
(Magma) [(8^n - 9*6^n + 15*5^n - 4*4^n - 9*3^n + 8*2^n - 2) / Factorial(3) : n in [0..25]]; // G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A032263, A036239, A051112.

Sequence in context: A024436 A042744 A020980 * A020975 A277877 A279870

Adjacent sequences: A051300 A051301 A051302 * A051304 A051305 A051306

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

Status

approved