A331772 a(n) = Sum_{-n

0, 0, 16, 48, 120, 224, 424, 688, 1096, 1600, 2392, 3344, 4568, 5984, 7976, 10256, 13112, 16320, 20360, 24848, 30136, 35936, 43208, 51152, 60184, 69952, 81800, 94576, 109000, 124448, 141944, 160592, 181480, 203648, 229400, 256688, 286424, 317792

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

When divided by 8 this becomes A331773.

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),n=1..50)];

Mathematica

A331772[n_]:=Sum[If[GCD[i,j]==2,If[i==j,4(n-i)^2,8(n-i)(n-j)],0],{i,2,n-1,2},{j,2,i,2}]+If[n>2,4n(n-2),0];Array[A331772,50] (* Paolo Xausa, Oct 18 2023 *)