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A051375 Number of Boolean functions of n variables and rank 3 from Post class F(5,inf). 1
0, 0, 9, 66, 345, 1590, 6909, 29106, 120465, 493230, 2005509, 8116746, 32744985, 131801670, 529647309, 2125861986, 8525167905, 34165634910, 136857036309, 548010848826, 2193789933225, 8780396200950, 35137287916509 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
V. Jovovic, 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).
LINKS
Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
FORMULA
a(n) = A036239(n) - A000918(n).
a(n) = (4^n - 3^n - 3*2^n + 5)/2.
a(n) = Sum_{j=1..n} (-1)^(j+1)*C(n, j)*C(2^(n-j)-1, k-1) (with k=3).
Also: 1/(k-1)!*Sum(s(k, j)*(2^((j-1)*n)-(2^(j-1)-1)^n), j=1..k), where s(k, j) are Stirling numbers of the first kind (with k=3).
From Colin Barker, Jun 25 2012: (Start)
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).
G.f.: 3*x^3*(3-8*x)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). (End)
MATHEMATICA
Table[(4^n - 3^n - 3*2^n + 5)/2, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
PROG
(PARI) for(n=0, 50, print1((4^n - 3^n - 3*2^n + 5)/2, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(4^n - 3^n - 3*2^n + 5)/2: n in [0..50]]; // G. C. Greubel, Oct 08 2017
CROSSREFS
Cf. A036240.
Sequence in context: A122733 A118465 A279129 * A081902 A002695 A003408
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda
EXTENSIONS
More terms from James A. Sellers
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)