The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 1

%I #13 Oct 08 2018 03:49:10

%S 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,

%T 148,92,12,14,122,210,262,262,210,122,14,16,156,280,376,400,376,280,

%U 156,16,18,194,362,502,578,578,502,362,194,18,20,236,452,652,772,836,772,652,452,236,20

%N 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.

%H Max A. Alekseyev. <a href="http://arXiv.org/abs/math.CO/0602511">On the number of two-dimensional threshold functions</a>. SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184

%t V[m_, n_] := Sum[If[GCD[i, j] == 1, (m-i+1)(n-j+1), 0], {i, m}, {j, n}];

%t T[m_, n_] := 2(2m n + m + n + 2 V[m, n]);

%t Table[T[m-n, n], {m, 0, 10}, {n, 0, m}] // Flatten (* _Jean-François Alcover_, Oct 08 2018 *)

%Y Twice A115009, which see for further information.

%K nonn,tabl

%O 0,2

%A _N. J. A. Sloane_, Feb 24 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)