A244840 Denominators of the triangle T(n,k) = (n*(n+1)/2+k+1)/(k+1) for n >= k >= 0.
1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 5, 2, 1, 1, 1, 3, 1, 5, 3, 1, 2, 1, 1, 1, 1, 5, 1, 7, 2, 1, 1, 2, 1, 4, 1, 2, 7, 8, 1, 2, 1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 1, 1, 1, 1, 2, 5, 1, 7, 4, 3, 5, 1, 2
Offset: 0
Examples
T(0,0) = 1/1, T(1,0) = 2/1, T(1,1) = 3/2,... . The triangle a(n,k) begins: n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... 0: 1 1: 1 2 2: 1 2 1 3: 1 1 1 2 4: 1 1 3 2 1 5: 1 2 1 4 1 2 6: 1 2 1 4 5 2 1 7: 1 1 3 1 5 3 1 2 8: 1 1 1 1 5 1 7 2 1 9: 1 2 1 4 1 2 7 8 1 2 10: 1 2 3 4 1 6 7 8 9 2 1 11: 1 1 1 2 5 1 7 4 3 5 1 2 12: 1 1 1 2 5 1 7 4 3 5 11 2 1 13: 1 2 3 4 5 6 1 8 9 10 11 12 1 2 14: 1 2 1 4 1 2 1 8 3 2 11 4 13 2 1 15: 1 1 1 1 1 1 7 1 3 1 11 1 13 7 1 2 16: 1 1 3 1 5 3 7 1 9 5 11 3 13 7 15 2 1 17: 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5 16 1 2 18: 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5 16 17 2 1 19: 1 1 3 2 1 3 7 4 9 1 11 6 13 7 3 8 17 9 1 2 20: 1 1 1 2 1 1 1 4 3 1 11 2 13 1 1 8 17 3 19 2 1 n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... .. reformatted - _Wolfdieter Lang_, Jul 28 2014 . The second column is of period 4: repeat 2, 2, 1, 1. From A014695 or A130658. The third column is of period 3: repeat 1, 1, 3. From A109007. The fourth column is of period 8: repeat 2, 2, 4, 4, 1, 1, 4, 4. The fifth column is of period 5: repeat 1, 1, 5, 5, 5. The sixth column is of period 12: repeat 2, 2, 3, 1, 2, 6, 1, 1, 6, 2, 1, 3 . The seventh column is of period 7: repeat 1, 1, 7, 7, 7, 7, 7. Hence the positive terms of A022998. Main diagonal: A000034(n). Alternate main and second diagonal: A130658(n). Common denominator by row: 1, 2, 2, 2, 6, 4, 20, 30, 70, ... .
Programs
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Mathematica
Table[(n*(n+1)/2+k+1)/(k+1) // Denominator, {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 08 2014 *)
Formula
a(n,k) = denominator((n*(n+1)/2 + k + 1)/(k+1)) for n >= k >= 0.
Extensions
Editse: Name reformulated, comment with T(n,k) reference added. - Wolfdieter Lang, Jul 28 2014
Comments