A051375 Number of Boolean functions of n variables and rank 3 from Post class F(5,inf).

0, 0, 9, 66, 345, 1590, 6909, 29106, 120465, 493230, 2005509, 8116746, 32744985, 131801670, 529647309, 2125861986, 8525167905, 34165634910, 136857036309, 548010848826, 2193789933225, 8780396200950, 35137287916509

Offset: 1

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

• easy
• nonn

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

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
• Index entries for sequences related to Boolean functions
• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Cf. A036240.

Programs

Magma

[(4^n - 3^n - 3*2^n + 5)/2: n in [0..50]]; // G. C. Greubel, Oct 08 2017

Mathematica

Table[(4^n - 3^n - 3*2^n + 5)/2, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

PARI

for(n=0,50, print1((4^n - 3^n - 3*2^n + 5)/2, ", ")) \\ G. C. Greubel, Oct 08 2017

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)

Extensions

More terms from James Sellers