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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. 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 (list; table; graph; refs; listen; history; text; internal format)
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 * A258249 A256448 A056756

Adjacent sequences:  A332360 A332361 A332362 * A332364 A332365 A332366

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 11 2020

STATUS

approved

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Last modified September 16 08:18 EDT 2021. Contains 347469 sequences. (Running on oeis4.)