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.
1, 2, 7, 3, 11, 19, 4, 18, 31, 51, 5, 24, 42, 69, 95, 6, 33, 59, 98, 135, 191, 7, 41, 74, 124, 172, 243, 311, 8, 52, 94, 158, 219, 310, 397, 507, 9, 62, 114, 191, 265, 376, 482, 615, 747, 10, 75, 138, 233, 325, 462, 593, 758, 921, 1135
Offset: 2
Examples
Triangle begins: 1, 2, 7, 3, 11, 19, 4, 18, 31, 51, 5, 24, 42, 69, 95, 6, 33, 59, 98, 135, 191, 7, 41, 74, 124, 172, 243, 311, 8, 52, 94, 158, 219, 310, 397, 507, 9, 62, 114, 191, 265, 376, 482, 615, 747, 10, 75, 138, 233, 325, 462, 593, 758, 921, 1135, ...
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 u01:=(m,n) -> 2*VQ(m/2,n/2,1)+2-VS(m,n); # This sequence for m from 2 to 12 do lprint([seq(u01(m,n),n=2..m)]); od: