OFFSET
3,1
REFERENCES
V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
a(n) = C(n + 6, 6) - 6*C(n + 4, 4) + 6*C(n + 3, 3) + 3*C(n + 2, 2) - 6*C(n + 1, 1) + 2*C(n, 0).
a(0)=2, a(1)=17, a(2)=71, a(3)=212, a(4)=518, a(5)=1106, a(6)=2142, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Jul 12 2011
G.f.: (-2-3*x+6*x^2-2*x^3)/(x-1)^7. - Harvey P. Dale, Jul 12 2011
a(n) = n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720. - Charles R Greathouse IV, Feb 19 2017
MAPLE
A056074:=n->n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: seq(A056074(n), n=3..60); # Wesley Ivan Hurt, Oct 06 2017
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2, 17, 71, 212, 518, 1106, 2142}, 30] (* or *) Table[Binomial[n+6, 6]-6Binomial[n+4, 4]+6Binomial[n+3, 3]+ 3Binomial[n+2, 2]- 6Binomial[n+1, 1]+ 2Binomial[n, 0], {n, 3, 30}] (* Harvey P. Dale, Jul 12 2011 *)
PROG
(PARI) a(n)=n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720 \\ Charles R Greathouse IV, Feb 19 2017
(Magma) [n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: n in [3..25]]; // G. C. Greubel, Oct 06 2017
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 26 2000
STATUS
approved