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A244734 Numerators of the triangle T(n,k) = (n*(n+1)/2 + k + 1)/(k+1) for n >= k >= 0. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

LINKS

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

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A244840 (denominators).

Sequence in context: A308201 A026362 A223490 * A230089 A081811 A304181

Adjacent sequences:  A244731 A244732 A244733 * A244735 A244736 A244737

KEYWORD

nonn,tabl,easy

AUTHOR

Paul Curtz, Jul 05 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

STATUS

approved

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Last modified December 6 03:33 EST 2021. Contains 349562 sequences. (Running on oeis4.)