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A331762 Triangle read by rows: T(n,k) (1 <= k <= n) = Sum_{i=1..n, j=1..k, gcd(i,j)=2} (n+1-i)*(k+1-j).

%I A331762 #18 Jul 02 2020 05:07:20
%S A331762 0,0,1,0,2,4,0,4,8,15,0,6,12,22,32,0,9,18,33,48,71,0,12,24,44,64,94,
%T A331762 124,0,16,32,58,84,123,162,211,0,20,40,72,104,152,200,260,320,0,25,50,
%U A331762 90,130,190,250,325,400,499
%N A331762 Triangle read by rows: T(n,k) (1 <= k <= n) = Sum_{i=1..n, j=1..k, gcd(i,j)=2} (n+1-i)*(k+1-j).
%H A331762 M. 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:<a href="http://dx.doi.org/10.1137/090750184">10.1137/090750184</a>
%H A331762 M. A. Alekseyev, M. Basova, N. Yu. Zolotykh. <a href="http://dx.doi.org/10.1137/140978090">On the minimal teaching sets of two-dimensional threshold functions</a>. SIAM J. Disc. Math. 29(1), 2015, pp. 157-165.
%e A331762 Triangle begins:
%e A331762   0;
%e A331762   0,  1;
%e A331762   0,  2,  4;
%e A331762   0,  4,  8,  15;
%e A331762   0,  6, 12,  22,  32;
%e A331762   0,  9, 18,  33,  48,  71;
%e A331762   0, 12, 24,  44,  64,  94, 124;
%e A331762   0, 16, 32,  58,  84, 123, 162, 211;
%e A331762   0, 20, 40,  72, 104, 152, 200, 260, 320;
%e A331762   0, 25, 50,  90, 130, 190, 250, 325, 400, 499;
%e A331762   0, 30, 60, 108, 156, 228, 300, 390, 480, 598, 716;
%e A331762   ...
%p A331762 V := proc(m,n,q) local a,i,j; a:=0;
%p A331762 for i from 1 to m do for j from 1 to n do
%p A331762 if gcd(i,j)=q then a:=a+(m+1-i)*(n+1-j); fi; od: od: a; end;
%p A331762 for m from 1 to 12 do
%p A331762 lprint([seq(V(m,n,2),n=1..m)]); od:
%t A331762 Table[Sum[Boole[GCD[i, j] == 2] (n + 1 - i) (k + 1 - j), {i, n}, {j, k}], {n, 11}, {k, n}] // Flatten (* _Michael De Vlieger_, Feb 04 2020 *)
%Y A331762 Cf. A115004, A114999, A320541.
%Y A331762 The main diagonal is A331761.
%Y A331762 See A335683 for another version.
%K A331762 nonn,tabl
%O A331762 1,5
%A A331762 _N. J. A. Sloane_, Feb 04 2020