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

1,3

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A000918, A036239, A036240.

Sequence in context: A239426 A157086 A366306 * A101721 A173582 A065973

Adjacent sequences: A051373 A051374 A051375 * A051377 A051378 A051379

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda

Extensions

More terms from James A. Sellers

Status

approved