

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.


0



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, 12, 16, 19, 24, 28, 28, 4, 9, 13, 16, 22, 27, 31, 36, 36, 5, 10, 15, 20, 25, 30, 35, 40, 45, 45, 5, 10, 15, 22, 25, 33, 37, 43, 49, 55, 55, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 66
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OFFSET

2,5


COMMENTS

T(n,n) = T(n,n1) because all grid points with m = n lie on a side of the triangle and thus not strictly inside.


LINKS



EXAMPLE

The triangle begins:
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, 12, 16, 19, 24, 28, 28;
4, 9, 13, 16, 22, 27, 31, 36, 36;
5, 10, 15, 20, 25, 30, 35, 40, 45, 45;
5, 10, 15, 22, 25, 33, 37, 43, 49, 55, 55


PROG

(PARI) T(n, m) = sum(i=1, n1, sum(j=1, m1, (i/j > n/m))); \\ Michel Marcus, Jun 07 2022


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



