A244734 Numerators of the triangle T(n,k) = (n*(n+1)/2 + k + 1)/(k+1) for n >= k >= 0.

1, 2, 3, 4, 5, 2, 7, 4, 3, 5, 11, 6, 13, 7, 3, 16, 17, 6, 19, 4, 7, 22, 23, 8, 25, 26, 9, 4, 29, 15, 31, 8, 33, 17, 5, 9, 37, 19, 13, 10, 41, 7, 43, 11, 5, 46, 47, 16, 49, 10, 17, 52, 53, 6, 11, 56, 57, 58, 59, 12, 61, 62, 63, 64, 13, 6, 67, 34, 23, 35, 71, 12, 73, 37, 25, 38, 7, 13

Offset: 0

Author

Paul Curtz, Jul 05 2014

Keywords

• nonn
• tabl
• easy

Comments

The rational triangle T(n,k) begins:

n\k 0 1 2 3 4 5 6 7 8 9 ...

0: 1

1: 2 3/2

2: 4 5/2 2

3: 7 4 3 5/2

4: 11 6 13/3 7/2 3

5: 16 17/2 6 19/4 4 7/2

6: 22 23/2 8 25/4 26/5 9/2 4

7: 29 15 31/3 8 33/5 17/3 5 9/2

8: 37 19 13 10 41/5 7 43/7 11/2 5

9: 46 47/2 16 49/4 10 17/2 52/7 53/8 6 11/2

... reformatted and formula corrected. - Wolfdieter Lang, Jul 28 2014

Examples

			The triangle a(n,k) begins:
n\k   0   1   2   3   4   5   6   7  8   9 ...
0:    1
1:    2   3
2:    4   5   2
3:    7   4   3   5
4:   11   6  13   7   3
5:   16  17   6  19   4   7
6:   22  23   8  25  26   9   4
7:   29  15  31   8  33  17   5   9
8:   37  19  13  10  41   7  43  11  5
9:   46  47  16  49  10  17  52  53  6  11
... reformatted - _Wolfdieter Lang_, Jul 28 2014
First column: A000124. Main diagonal: A145051 from A026741.
Alternate main and second diagonal: in A173234.
		

Crossrefs

Cf. A244840 (denominators).

Programs

Mathematica

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

Formula

a(n,k) = numerator((n*(n+1)/2+k+1)/(k+1)), n >= k >= 0. -Wolfdieter Lang, Jul 28 2014

Extensions

Edited: (wrong) name changed. Offset changed to 0 in order to fit with the denominators A244840 and the Mathematica program. Cf. A244840 added. - Wolfdieter Lang, Jul 28 2014