A331773 a(n) = Sum_{-n<i<n, -n<j<n, gcd{i,j}=2} (n-|i|)*(n-|j|)/8.

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

1,3

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)/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 *)

Crossrefs

Equals A331772/8.

Sequence in context: A256313 A138621 A163061 * A033286 A182724 A342163

Adjacent sequences: A331770 A331771 A331772 * A331774 A331775 A331776

Keyword

nonn

Author

N. J. A. Sloane, Feb 08 2020

Status

approved