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

0,3

Comments

Numerators: A244734(n,k).

See A244734 for the first entries of the rational triangle T(n,k).

Links

Table of n, a(n) for n=0..77.

Formula

a(n,k) = denominator((n*(n+1)/2 + k + 1)/(k+1)) for n >= k >= 0.

Example

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, ... .

Mathematica

Table[(n*(n+1)/2+k+1)/(k+1) // Denominator, {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 08 2014 *)

Crossrefs

Cf. A014695, A130658, A109007, A002260, A022998, A244734, A000034.

Sequence in context: A136044 A375736 A184240 * A103414 A092400 A303598

Adjacent sequences: A244837 A244838 A244839 * A244841 A244842 A244843

Keyword

nonn,frac,tabl,easy

Author

Paul Curtz, Jul 07 2014

Extensions

Editse: Name reformulated, comment with T(n,k) reference added. - Wolfdieter Lang, Jul 28 2014

Status

approved