A331772 a(n) = Sum_{-n<i<n, -n<j<n, gcd{i,j}=2} (n-|i|)*(n-|j|).

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

1,3

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.

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 *)

Crossrefs

When divided by 8 this becomes A331773.

Sequence in context: A023648 A098322 A175164 * A190112 A211576 A211590

Adjacent sequences: A331769 A331770 A331771 * A331773 A331774 A331775

Keyword

nonn

Author

N. J. A. Sloane, Feb 08 2020

Status

approved