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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-Fran├žois 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

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