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A332363 Triangle read by rows: T(m,n) = number of unstable threshold functions (the function u_{0,1}(m,n) of Alekseyev et al. 2015) for m >= n >= 2.

%I A332363 #22 Feb 13 2020 00:58:36
%S A332363 1,2,7,3,11,19,4,18,31,51,5,24,42,69,95,6,33,59,98,135,191,7,41,74,
%T A332363 124,172,243,311,8,52,94,158,219,310,397,507,9,62,114,191,265,376,482,
%U A332363 615,747,10,75,138,233,325,462,593,758,921,1135
%N A332363 Triangle read by rows: T(m,n) = number of unstable threshold functions (the function u_{0,1}(m,n) of Alekseyev et al. 2015) for m >= n >= 2.
%H A332363 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 A332363 Triangle begins:
%e A332363 1,
%e A332363 2, 7,
%e A332363 3, 11, 19,
%e A332363 4, 18, 31, 51,
%e A332363 5, 24, 42, 69, 95,
%e A332363 6, 33, 59, 98, 135, 191,
%e A332363 7, 41, 74, 124, 172, 243, 311,
%e A332363 8, 52, 94, 158, 219, 310, 397, 507,
%e A332363 9, 62, 114, 191, 265, 376, 482, 615, 747,
%e A332363 10, 75, 138, 233, 325, 462, 593, 758, 921, 1135,
%e A332363 ...
%p A332363 VQ := proc(m,n,q) local eps,a,i,j; eps := 10^(-6); a:=0;
%p A332363 for i from ceil(-m+eps) to floor(m-eps) do
%p A332363 for j from ceil(-n+eps) to floor(n-eps) do
%p A332363 if gcd(i,j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
%p A332363 VS := proc(m,n) local a,i,j; a:=0;
%p A332363 for i from 1 to m-1 do for j from 1 to n-1 do
%p A332363 if gcd(i,j)=1 then a:=a+1; fi; od: od: a; end; # A331781
%p A332363 u01:=(m,n) -> 2*VQ(m/2,n/2,1)+2-VS(m,n); # This sequence
%p A332363 for m from 2 to 12 do lprint([seq(u01(m,n),n=2..m)]); od:
%Y A332363 Cf. A332350, A332352, A331781.
%Y A332363 Main diagonal is A332364.
%K A332363 nonn,tabl
%O A332363 2,2
%A A332363 _N. J. A. Sloane_, Feb 11 2020