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A245251 Triangle T(a,b) read by rows: sum_{k=1..a-1} floor(k*b/a).

%I A245251 #15 Nov 29 2014 05:43:30
%S A245251 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 A245251 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 A245251 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 A245251 Triangle T(a,b) read by rows: sum_{k=1..a-1} floor(k*b/a).
%F A245251 T(a, b) = (a*b-a-b+gcd(a,b))/2.
%F A245251 T(n, n) = n*(n-1)/2.
%e A245251   0;
%e A245251   0   1;
%e A245251   0   1   3;
%e A245251   0   2   3   6;
%e A245251   0   2   4   6  10;
%e A245251   0   3   6   8  10  15;
%e A245251   0   3   6   9  12  15  21;
%e A245251   0   4   7  12  14  18  21  28;
%e A245251   0   4   9  12  16  21  24  28  36;
%e A245251   0   5   9  14  20  23  27  32  36  45;
%t A245251 Table[Sum[Floor[(k b)/a], {k, a-1}], {a, 20}, {b, a}] // Flatten
%Y A245251 Cf. A000217 (right diagonal).
%K A245251 nonn,tabl,easy
%O A245251 1,6
%A A245251 _Jaimal Ichharam_, Jul 15 2014