A047707 Number of monotone Boolean functions of n variables with 3 mincuts. Also Sperner systems with 3 blocks.

0, 0, 0, 2, 64, 1090, 14000, 153762, 1533504, 14356610, 128722000, 1119607522, 9528462944, 79817940930, 660876543600, 5424917141282, 44246078560384, 359144709794050, 2904688464582800, 23429048035827042, 188593339362097824

Offset

0,4

Comments

The paper by G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), mentions many sequences, but since only very condensed formulas are given, it is hard to match them with entries in the OEIS. It would be nice to add this reference to all the sequences that it mentions. - N. J. A. Sloane, Jan 01 2016

Term a(1108) has 1000 decimal digits. - Michael De Vlieger, Jan 26 2016

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 292, #8, s(n,3).

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1107

K. S. Brown, Dedekind's problem.

Vladeta Jovovic, Illustration for A016269, A047707, A051112-A051118

G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), 69-87 DOI: 10.2298/PIM140406001K. See page 86, formula for alpha^hat(3,n).

Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.

Index entries for sequences related to Boolean functions

Index entries for linear recurrences with constant coefficients, signature (28,-315,1820,-5684,9072,-5760).

Formula

a(n) = (2^n)*(2^n - 1)*(2^n - 2)/6 - (6^n - 5^n - 4^n + 3^n).

G.f.: -2*x^3*(36*x^2-4*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 31 2012

a(n) = Binomial(2^n,3) - (6^n - 5^n - 4^n + 3^n). - Ross La Haye, Jan 26 2016

Mathematica

Table[Binomial[2^n, 3] - (6^n - 5^n - 4^n + 3^n), {n, 20}] (* or *)
CoefficientList[Series[-2 x^3 (36 x^2 - 4 x - 1)/((2 x - 1) (3 x - 1) (4 x - 1) (5 x - 1) (6 x - 1) (8 x - 1)), {x, 0, 20}], x] (* Michael De Vlieger, Jan 26 2016 *)

Prog

(PARI) a(n)=binomial(2^n, 3)-(6^n-5^n-4^n+3^n) \\ Charles R Greathouse IV, Apr 08 2016

Crossrefs

Cf. A016269, A051112.

Sequence in context: A299063 A299835 A299724 * A223121 A134939 A217268

Adjacent sequences: A047704 A047705 A047706 * A047708 A047709 A047710

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved