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A354698 T(n,k) is the number of points with integer coordinates strictly inside the triangle with vertices (0,0), (n,0), (n,k), where T(n,k) is a triangle read by rows, 2 <= k <= n.

%I A354698 #16 Jun 08 2022 10:16:18
%S A354698 0,1,1,1,3,3,2,4,6,6,2,4,7,10,10,3,6,9,12,15,15,3,7,9,14,17,21,21,4,7,
%T A354698 12,16,19,24,28,28,4,9,13,16,22,27,31,36,36,5,10,15,20,25,30,35,40,45,
%U A354698 45,5,10,15,22,25,33,37,43,49,55,55,6,12,18,24,30,36,42,48,54,60,66,66
%N A354698 T(n,k) is the number of points with integer coordinates strictly inside the triangle with vertices (0,0), (n,0), (n,k), where T(n,k) is a triangle read by rows, 2 <= k <= n.
%C A354698 T(n,n) = T(n,n-1) because all grid points with m = n lie on a side of the triangle and thus not strictly inside.
%e A354698 The triangle begins:
%e A354698   0;
%e A354698   1,  1;
%e A354698   1,  3,  3;
%e A354698   2,  4,  6,  6;
%e A354698   2,  4,  7, 10, 10;
%e A354698   3,  6,  9, 12, 15, 15;
%e A354698   3,  7,  9, 14, 17, 21, 21;
%e A354698   4,  7, 12, 16, 19, 24, 28, 28;
%e A354698   4,  9, 13, 16, 22, 27, 31, 36, 36;
%e A354698   5, 10, 15, 20, 25, 30, 35, 40, 45, 45;
%e A354698   5, 10, 15, 22, 25, 33, 37, 43, 49, 55, 55
%o A354698 (PARI) T(n, m) = sum(i=1, n-1, sum(j=1, m-1, (i/j > n/m))); \\ _Michel Marcus_, Jun 07 2022
%Y A354698 Cf. A000217 (right diagonal), A074148 (3rd diagonal).
%Y A354698 Cf. A004526 (column 2), A117571 (column 3).
%K A354698 nonn,tabl,easy
%O A354698 2,5
%A A354698 _Hugo Pfoertner_, Jun 06 2022