%I #15 Nov 29 2014 05:43:30
%S 0,0,1,0,1,3,0,2,3,6,0,2,4,6,10,0,3,6,8,10,15,0,3,6,9,12,15,21,0,4,7,
%T 12,14,18,21,28,0,4,9,12,16,21,24,28,36,0,5,9,14,20,23,27,32,36,45,0,
%U 5,10,15,20,25,30,35,40,45,55,0,6,12,18,22,30,33,40,45,50,55,66,0,6,12,18,24,30,36,45
%N Triangle T(a,b) read by rows: sum_{k=1..a-1} floor(k*b/a).
%F T(a, b) = (a*b-a-b+gcd(a,b))/2.
%F T(n, n) = n*(n-1)/2.
%e 0;
%e 0 1;
%e 0 1 3;
%e 0 2 3 6;
%e 0 2 4 6 10;
%e 0 3 6 8 10 15;
%e 0 3 6 9 12 15 21;
%e 0 4 7 12 14 18 21 28;
%e 0 4 9 12 16 21 24 28 36;
%e 0 5 9 14 20 23 27 32 36 45;
%t Table[Sum[Floor[(k b)/a], {k, a-1}], {a, 20}, {b, a}] // Flatten
%Y Cf. A000217 (right diagonal).
%K nonn,tabl,easy
%O 1,6
%A _Jaimal Ichharam_, Jul 15 2014
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