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A354698
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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.
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0
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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
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2,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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PROG
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(PARI) T(n, m) = sum(i=1, n-1, sum(j=1, m-1, (i/j > n/m))); \\ Michel Marcus, Jun 07 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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