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

%I A051375 #25 Jul 02 2025 16:01:58
%S A051375 0,0,9,66,345,1590,6909,29106,120465,493230,2005509,8116746,32744985,
%T A051375 131801670,529647309,2125861986,8525167905,34165634910,136857036309,
%U A051375 548010848826,2193789933225,8780396200950,35137287916509
%N A051375 Number of Boolean functions of n variables and rank 3 from Post class F(5,inf).
%D A051375 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).
%H A051375 G. C. Greubel, <a href="/A051375/b051375.txt">Table of n, a(n) for n = 1..1000</a>
%H A051375 Thomas Wieder, The number of certain k-combinations of an n-set, <a href="http://www.math.nthu.edu.tw/~amen/">Applied Mathematics Electronic Notes</a>, vol. 8 (2008).
%H A051375 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H A051375 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A051375 a(n) = A036239(n) - A000918(n).
%F A051375 a(n) = (4^n - 3^n - 3*2^n + 5)/2.
%F A051375 a(n) = Sum_{j=1..n} (-1)^(j+1)*C(n, j)*C(2^(n-j)-1, k-1) (with k=3).
%F A051375 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).
%F A051375 From _Colin Barker_, Jun 25 2012: (Start)
%F A051375 a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).
%F A051375 G.f.: 3*x^3*(3-8*x)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)). (End)
%t A051375 Table[(4^n - 3^n - 3*2^n + 5)/2, {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o A051375 (PARI) for(n=0,50, print1((4^n - 3^n - 3*2^n + 5)/2, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o A051375 (Magma) [(4^n - 3^n - 3*2^n + 5)/2: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y A051375 Cf. A036240.
%K A051375 easy,nonn
%O A051375 1,3
%A A051375 _Vladeta Jovovic_, Goran Kilibarda
%E A051375 More terms from _James Sellers_