A332353 Triangle read by rows: T(m,n) = Sum_{-m= n >= 1.

0, 0, 0, 1, 2, 8, 2, 4, 14, 24, 3, 6, 22, 38, 60, 4, 8, 30, 52, 82, 112, 5, 10, 40, 70, 112, 154, 212, 6, 12, 50, 88, 142, 196, 270, 344, 7, 14, 62, 110, 178, 246, 340, 434, 548, 8, 16, 74, 132, 214, 296, 410, 524, 662, 800, 9, 18, 88, 158, 258, 358, 498, 638, 808, 978, 1196

Offset: 1

Author

N. J. A. Sloane, Feb 10 2020

Keywords

• nonn
• tabl

Comments

This is the triangle in A332352, halved.

Examples

			Triangle begins:
0,
0, 0,
1, 2, 8,
2, 4, 14, 24,
3, 6, 22, 38, 60,
4, 8, 30, 52, 82, 112,
5, 10, 40, 70, 112, 154, 212,
6, 12, 50, 88, 142, 196, 270, 344,
7, 14, 62, 110, 178, 246, 340, 434, 548,
8, 16, 74, 132, 214, 296, 410, 524, 662, 800,
...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of the triangle, flattened)
• 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. This sequence is f_2(m,n)/2.

Crossrefs

The main diagonal is A177719.

Cf. A332350, A332352.

Programs

Maple

VR := proc(m,n,q) local a,i,j; a:=0;
for i from -m+1 to m-1 do for j from -n+1 to n-1 do
if gcd(i,j)=q then a:=a+(m-abs(i))*(n-abs(j)); fi; od: od: a; end;
for m from 1 to 12 do lprint(seq(VR(m,n,2)/2,n=1..m),); od:

Mathematica

A332353[m_,n_]:=Sum[If[GCD[i,j]==2,2(m-i)(n-j),0],{i,2,m-1,2},{j,2,n-1,2}]+If[n>2,m*n-2m,0]+If[m>2,m*n-2n,0];Table[A332353[m, n],{m,15},{n, m}] (* Paolo Xausa, Oct 18 2023 *)