A134061 Triangle read by rows: T(n,k) = A124928(n,k) + A134059(n,k) - A007318(n,k).
1, 3, 5, 3, 10, 5, 3, 15, 15, 5, 3, 20, 30, 20, 5, 3, 25, 50, 50, 25, 5, 3, 30, 75, 100, 75, 30, 5, 3, 35, 105, 175, 175, 105, 35, 5, 3, 40, 140, 280, 350, 280, 140, 40, 5, 3, 45, 180, 420, 630, 630, 420, 180, 45, 5, 3, 50, 225, 600, 1050, 1260, 1050, 600, 225, 50, 5
Offset: 0
Examples
First few rows of the triangle: 1; 3, 5; 3, 10, 5; 3, 15, 15, 5; 3, 20, 30, 20, 5; 3, 25, 50, 50, 25, 5; ...
Programs
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Mathematica
Table[If[k > 0, 3*Binomial[n, k], 1] + 2*Binomial[n, k] - 2*Boole[n == 0], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 31 2025 *)
Formula
T(n,k) = 5*binomial(n,k) if k > 0, (0 <= k <= n), with leftmost column = (1,3,3,3,...).
Extensions
More terms from Amiram Eldar, May 31 2025
Comments