A244494 - OEIS

%I #11 Mar 24 2021 06:10:16

%S 2,6,70,870,36518,1828134,300503590,60273667110,39431461330982,

%T 31648840352155686,82716718794775795750,265590372390118027343910,

%U 2775704953984257023035176998,35650312393325457366304103888934,1490221075739321877604231759426844710

%N Number of quadratic balanced Boolean functions of n variables.

%H Thomas W. Cusick and Yuri L. Borissov, <a href="https://doi.org/10.1016/j.disc.2010.08.016">A refinement of Cusick-Cheon bound for the second order binary Reed-Muller code</a>, Discrete Math. 310 (2010), no. 24, 3537--3543. MR2734734 (2011j:94188).

%F See Maple code.

%p f:=proc(n) add( 2^(h*(h+1)+1)*

%p mul( 2^(n-i)-1,i=0..2*h)/mul(2^(2*j)-1,j=1..h),

%p h=1..floor(n/2))+(2^(n+1)-2); end;

%p [seq(f(n),n=1..25)];

%t f[n_] := Sum[2^(h(h+1)+1) Product[2^(n-i)-1, {i, 0, 2h}]/

%t      Product[2^(2j)-1, {j, 1, h}], {h, 1, n/2}]+(2^(n+1)-2);

%t Array[f, 25] (* _Jean-François Alcover_, Mar 24 2021, after Maple code *)

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 05 2014