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A332365 Triangle read by rows: T(m,n) = number of threshold functions (the function u_{0,2}(m,n) of Alekseyev et al. 2015) for m >= n >= 2.

%I A332365 #13 Feb 13 2020 00:58:53
%S A332365 3,6,13,9,21,33,12,30,49,73,15,40,66,99,133,18,51,85,130,177,237,21,
%T A332365 63,106,164,224,301,381,24,76,130,202,277,374,475,593,27,90,154,241,
%U A332365 331,448,570,713,857,30,105,182,287,395,538,687,862,1039,1261,33,121,211,335,462,632,808,1016,1226,1489,1757
%N A332365 Triangle read by rows: T(m,n) = number of threshold functions (the function u_{0,2}(m,n) of Alekseyev et al. 2015) for m >= n >= 2.
%H A332365 M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. <a href="https://doi.org/10.1137/140978090">On the minimal teaching sets of two-dimensional threshold functions</a>. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. See Theorem 11.
%e A332365 Triangle begins:
%e A332365 3,
%e A332365 6, 13,
%e A332365 9, 21, 33,
%e A332365 12, 30, 49, 73,
%e A332365 15, 40, 66, 99, 133,
%e A332365 18, 51, 85, 130, 177, 237,
%e A332365 21, 63, 106, 164, 224, 301, 381,
%e A332365 24, 76, 130, 202, 277, 374, 475, 593,
%e A332365 27, 90, 154, 241, 331, 448, 570, 713, 857,
%e A332365 ...
%p A332365 VQ := proc(m,n,q) local eps,a,i,j; eps := 10^(-6); a:=0;
%p A332365 for i from ceil(-m+eps) to floor(m-eps) do
%p A332365 for j from ceil(-n+eps) to floor(n-eps) do
%p A332365 if gcd(i,j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
%p A332365 VS := proc(m,n) local a,i,j; a:=0;
%p A332365 for i from 1 to m-1 do for j from 1 to n-1 do
%p A332365 if gcd(i,j)=1 then a:=a+1; fi; od: od: a; end; # A331781
%p A332365 u02:=(m,n) -> VQ(m,n,2)+2-2*VQ(m/2,n/2,1)+VS(m,n); # This sequence
%p A332365 for m from 2 to 12 do lprint([seq(u02(m,n),n=2..m)]); od:
%Y A332365 Cf. A332350, A332352, A332363, A331781.
%Y A332365 Main diagonal is A332366.
%K A332365 nonn,tabl
%O A332365 2,1
%A A332365 _N. J. A. Sloane_, Feb 11 2020