A051360 - OEIS

%I #23 Sep 04 2021 12:49:05

%S 0,0,0,16,389,3112,16231,66177,228438,697219,1932601,4953493,11892484,

%T 27003029,58421782,121154728,241995312,467422242,875997590,1597434614,

%U 2841382379,4940146414,8411111897,14046656347,23041951126,37174397565,59052693975,92458885395

%N A class of Boolean functions of n variables and rank 4.

%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 T. D. Noe, <a href="/A051360/b051360.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

%F a(n) = n*(n-1)*(n-2)*(n^12 + 123*n^11 + 6947*n^10 + 238995*n^9 + 5406153*n^8 + 81325989*n^7 + 826126601*n^6 + 6015252225*n^5 + 31515483346*n^4 + 95237254188*n^3 + 64213530552*n^2-798617063520*n-2101517913600)/15!.

%F G.f.: -x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16) / (x -1)^16. - _Colin Barker_, Jul 11 2013

%t CoefficientList[Series[-x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16) / (x -1)^16, {x, 0, 50}], x] (* _G. C. Greubel_, Oct 07 2017 *)

%t LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{0,0,0,16,389,3112,16231,66177,228438,697219,1932601,4953493,11892484,27003029,58421782,121154728},40] (* _Harvey P. Dale_, Sep 04 2021 *)

%o (PARI) x='x+O('x^50); concat([0,0,0], Vec(-x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16)/(x -1)^16)) \\ _G. C. Greubel_, Oct 07 2017

%K nonn,easy

%O 0,4

%A _Vladeta Jovovic_, Goran Kilibarda