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A115010 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*m*n+m+n+2*V(m,n), for m >= 1, n >= 1. 1

%I #18 Nov 28 2017 08:32:56

%S 6,13,13,22,28,22,33,49,49,33,46,74,86,74,46,61,105,131,131,105,61,78,

%T 140,188,200,188,140,78,97,181,251,289,289,251,181,97,118,226,326,386,

%U 418,386,326,226,118,141,277,409,503,559,559,503,409,277,141,166,332,502,632,730

%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*m*n+m+n+2*V(m,n), for m >= 1, n >= 1.

%H Max A. Alekseyev, <a href="https://arxiv.org/abs/math/0602511">On the number of two-dimensional threshold functions</a>, arXiv:math/0602511 [math.CO], 2006-2010; SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184

%p V:=proc(m,n) local t1,i,j; t1:=0; for i from 1 to m do for j from 1 to n do if gcd(i,j)=1 then t1:=t1+(m+1-i)*(n+1-j); fi; od; od; t1; end; T:=(m,n)->(2*m*n+m+n+2*V(m,n));

%t V[m_, n_] := Sum[Boole[CoprimeQ[i, j]]*(m-i+1)*(n-j+1), {i, m}, {j, n}];

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

%t Table[T[m - n + 1, n], {m, 1, 12}, {n, 1, m}] // Flatten (* _Jean-François Alcover_, Nov 28 2017 *)

%Y Cf. A114999, A114043, A115004, A115005, A115006, A115007.

%K nonn,tabl

%O 1,1

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

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)