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.
3, 6, 13, 9, 21, 33, 12, 30, 49, 73, 15, 40, 66, 99, 133, 18, 51, 85, 130, 177, 237, 21, 63, 106, 164, 224, 301, 381, 24, 76, 130, 202, 277, 374, 475, 593, 27, 90, 154, 241, 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
Offset: 2
Examples
Triangle begins: 3, 6, 13, 9, 21, 33, 12, 30, 49, 73, 15, 40, 66, 99, 133, 18, 51, 85, 130, 177, 237, 21, 63, 106, 164, 224, 301, 381, 24, 76, 130, 202, 277, 374, 475, 593, 27, 90, 154, 241, 331, 448, 570, 713, 857, ...
Links
- M. A. Alekseyev, M. Basova, and N. Yu. Zolotykh. On the minimal teaching sets of two-dimensional threshold functions. SIAM Journal on Discrete Mathematics 29:1 (2015), 157-165. doi:10.1137/140978090. See Theorem 11.
Programs
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Maple
VQ := proc(m,n,q) local eps,a,i,j; eps := 10^(-6); a:=0; for i from ceil(-m+eps) to floor(m-eps) do for j from ceil(-n+eps) to floor(n-eps) do if gcd(i,j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end; VS := proc(m,n) local a,i,j; a:=0; for i from 1 to m-1 do for j from 1 to n-1 do if gcd(i,j)=1 then a:=a+1; fi; od: od: a; end; # A331781 u02:=(m,n) -> VQ(m,n,2)+2-2*VQ(m/2,n/2,1)+VS(m,n); # This sequence for m from 2 to 12 do lprint([seq(u02(m,n),n=2..m)]); od: