A115011 Array read by antidiagonals: let V(m,n) = Sum_{i=1..m, j=1..n, gcd(i,j)=1} (m+1-i)*(n+1-j), then T(m,n) = 2*(2*m*n+m+n+2*V(m,n)), for m >= 0, n >= 0.

0, 2, 2, 4, 12, 4, 6, 26, 26, 6, 8, 44, 56, 44, 8, 10, 66, 98, 98, 66, 10, 12, 92, 148, 172, 148, 92, 12, 14, 122, 210, 262, 262, 210, 122, 14, 16, 156, 280, 376, 400, 376, 280, 156, 16, 18, 194, 362, 502, 578, 578, 502, 362, 194, 18, 20, 236, 452, 652, 772, 836, 772, 652, 452, 236, 20

Offset: 0

Author

N. J. A. Sloane, Feb 24 2006

Keywords

• nonn
• tabl

Links

• Max A. Alekseyev. On the number of two-dimensional threshold functions. SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184

Crossrefs

Twice A115009, which see for further information.

Programs

Mathematica

V[m_, n_] := Sum[If[GCD[i, j] == 1, (m-i+1)(n-j+1), 0], {i, m}, {j, n}];
T[m_, n_] := 2(2m n + m + n + 2 V[m, n]);
Table[T[m-n, n], {m, 0, 10}, {n, 0, m}] // Flatten (* Jean-François Alcover, Oct 08 2018 *)