A331773 a(n) = Sum_{-n

0, 0, 2, 6, 15, 28, 53, 86, 137, 200, 299, 418, 571, 748, 997, 1282, 1639, 2040, 2545, 3106, 3767, 4492, 5401, 6394, 7523, 8744, 10225, 11822, 13625, 15556, 17743, 20074, 22685, 25456, 28675, 32086, 35803, 39724, 44209, 48934, 54067, 59456, 65365

Offset: 1

Author

N. J. A. Sloane, Feb 08 2020

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000
• 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 p. 158.

Crossrefs

Equals A331772/8.

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;
[seq(VR(n,n,2)/8,n=1..50)];

Mathematica

A331773[n_]:=Sum[If[GCD[i,j]==2,If[i==j,(n-i)^2/2,(n-i)(n-j)],0],{i,2,n-1,2},{j,2,i,2}]+If[n>2,n(n-2)/2,0];Array[A331773,50] (* Paolo Xausa, Oct 18 2023 *)