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%I #22 Sep 08 2022 08:44:59
%S 0,0,3,134,1935,20830,198303,1776894,15402495,130890110,1098087903,
%T 9130126654,75412301055,619706950590,5071742430303,41369422556414,
%U 336511166127615,2730929153686270,22119108433729503,178853777028618174
%N Number of Boolean functions of n variables and rank 4 from Post class F(5,inf).
%H G. C. Greubel, <a href="/A051376/b051376.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (25,-241,1135,-2734,3160,-1344).
%F a(n) = A036240(n) - A036239(n) + A000918(n).
%F a(n) = (8^n - 7^n - 6*4^n + 6*3^n + 11*2^n - 17)/6.
%F a(n) = Sum_{j=1..n} (-1)^(j+1)*C(n, j)*C(2^(n-j)-1, k-1), where k=4.
%F 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).
%F 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
%t 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 *)
%o (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
%o (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
%Y Cf. A000918, A036239, A036240.
%K easy,nonn
%O 1,3
%A _Vladeta Jovovic_, Goran Kilibarda
%E More terms from _James A. Sellers_
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