A051376 Number of Boolean functions of n variables and rank 4 from Post class F(5,inf).

0, 0, 3, 134, 1935, 20830, 198303, 1776894, 15402495, 130890110, 1098087903, 9130126654, 75412301055, 619706950590, 5071742430303, 41369422556414, 336511166127615, 2730929153686270, 22119108433729503, 178853777028618174

Offset: 1

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• 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.
• V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
• Index entries for sequences related to Boolean functions
• Index entries for linear recurrences with constant coefficients, signature (25,-241,1135,-2734,3160,-1344).

Crossrefs

Cf. A000918, A036239, A036240.

Programs

Magma

[(8^n - 7^n - 6*4^n + 6*3^n + 11*2^n - 17)/6: n in [1..50]]; // G. C. Greubel, Oct 08 2017

Mathematica

Table[(8^n - 7^n - 6*4^n + 6*3^n + 11*2^n - 17)/6, {n, 1, 50}] (* G. C. Greubel, Oct 08 2017 *)

PARI

for(n=1,50, print1((8^n - 7^n - 6*4^n + 6*3^n + 11*2^n - 17)/6, ", ")) \\ G. C. Greubel, Oct 08 2017

Formula

a(n) = A036240(n) - A036239(n) + A000918(n).

a(n) = (8^n - 7^n - 6*4^n + 6*3^n + 11*2^n - 17)/6.

a(n) = Sum_{j=1..n} (-1)^(j+1)*C(n, j)*C(2^(n-j)-1, k-1), where k=4.

Also: 1/(k-1)!*Sum_{j=1..k} s(k, j)*(2^((j-1)*n)-(2^(j-1)-1)^n), where s(k, j) are Stirling numbers of the first kind (and k=4).

G.f.: x^3*(3 + 59*x - 692*x^2 + 1344*x^3) / ( (x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(8*x-1)*(7*x-1) ). - R. J. Mathar, Jun 13 2013

Extensions

More terms from James Sellers