%I #28 Sep 08 2022 08:44:59
%S 0,0,0,13,75,263,720,1688,3550,6882,12516,21615,35761,57057,88244,
%T 132834,195260,281044,396984,551361,754167,1017355,1355112,1784156,
%U 2324058,2997590,3831100,4854915,6103773,7617285,9440428,11624070,14225528,17309160,20946992,25219381
%N A class of Boolean functions of n variables and rank 3.
%D 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 Vincenzo Librandi, <a href="/A051361/b051361.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n) = n*(n-1)*(n-2)*(n^4+31*n^3+287*n^2+1499*n+2922)/7!.
%F a(0)=0, a(1)=0, a(2)=0, a(3)=13, a(4)=75, a(5)=263, a(6)=720, a(7)=1688, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+ 8*a(n-7)- a(n-8) [From Harvey P. Dale, Jul 19 2011]
%F G.f.: x^3*(2*x^4-12*x^3+27*x^2-29*x+13)/(x-1)^8. - _Colin Barker_, Jul 11 2013
%t With[{c7=7!},Table[n(n-1)(n-2)(n^4+31n^3+287n^2+1499n+2922)/c7, {n,0,40}]] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,0,0,13,75,263,720,1688},41](* _Harvey P. Dale_, Jul 19 2011 *)
%o (Magma) [n*(n-1)*(n-2)*(n^4+31*n^3+287*n^2+1499*n+2922)/Factorial(7): n in [0..35]]; // _Vincenzo Librandi_, Jul 20 2011
%o (PARI) for(n=0,50, print1(n*(n-1)*(n-2)*(n^4 +31*n^3 +287*n^2 +1499*n +2922)/7!, ", ")) \\ _G. C. Greubel_, Oct 07 2017
%K nonn,easy
%O 0,4
%A _Vladeta Jovovic_, Goran Kilibarda
%E More terms from _Colin Barker_, Jul 11 2013