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A115009 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 >= 0, n >= 0. 1

%I

%S 0,1,1,2,6,2,3,13,13,3,4,22,28,22,4,5,33,49,49,33,5,6,46,74,86,74,46,

%T 6,7,61,105,131,131,105,61,7,8,78,140,188,200,188,140,78,8,9,97,181,

%U 251,289,289,251,181,97,9,10,118,226,326,386,418,386,326,226,118,10,11,141,277

%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 >= 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

%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[If[GCD[i, j] == 1, (m-i+1)*(n-j+1), 0], {i, 1, m}, {j, 1, n}]; T[m_, n_] := 2*m*n+m+n+2*V[m, n]; Table[T[m-n, n], {m, 0, 11}, {n, 0, m}] // Flatten (* _Jean-Fran├žois Alcover_, Jan 08 2014 *)

%Y Cf. A114999, A114043, A115004, A115005, A115006, A115007, A115010, A115011.

%K nonn,tabl

%O 0,4

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

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Last modified May 6 07:01 EDT 2021. Contains 343580 sequences. (Running on oeis4.)