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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. 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 COMMENTS 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. LINKS Table of n, a(n) for n=2..79. 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, n-1, sum(j=1, m-1, (i/j > n/m))); \\ Michel Marcus, Jun 07 2022 CROSSREFS Cf. A000217 (right diagonal), A074148 (3rd diagonal). Cf. A004526 (column 2), A117571 (column 3). Sequence in context: A349661 A282545 A306471 * A050610 A151848 A238238 Adjacent sequences: A354695 A354696 A354697 * A354699 A354700 A354701 KEYWORD nonn,tabl,easy AUTHOR Hugo Pfoertner, Jun 06 2022 STATUS approved

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Last modified December 11 06:34 EST 2023. Contains 367717 sequences. (Running on oeis4.)