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

2,2

Links

Table of n, a(n) for n=2..56.

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.

Example

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,
...

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:

Crossrefs

Cf. A332350, A332352, A331781.

Main diagonal is A332364.

Sequence in context: A185510 A304754 A091578 * A353408 A365966 A258249

Adjacent sequences: A332360 A332361 A332362 * A332364 A332365 A332366

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 11 2020

Status

approved