A332363 -id:A332363 - cp's OEIS frontend

A332364 Main diagonal of A332363.

1, 7, 19, 51, 95, 191, 311, 507, 747, 1135, 1591, 2195, 2879, 3863, 4987, 6399, 7971, 9979, 12187, 14815, 17691, 21307, 25235, 29735, 34579, 40479, 46831, 54019, 61687, 70419, 79683, 90095, 101139, 113983, 127579, 142423, 158035, 175939, 194791

Offset: 2

N. J. A. Sloane, Feb 12 2020

nonn

Cf. A332363.

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.

Original entry on oeis.org

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

N. J. A. Sloane, Feb 11 2020

			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,
...

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.

Cf. A332350, A332352, A332363, A331781.

Main diagonal is A332366.

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:

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A332364 Main diagonal of A332363.

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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.

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