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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
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: A026362 A223490 A354749 * A230089 A081811 A304181
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 July 17 21:15 EDT 2024. Contains 374377 sequences. (Running on oeis4.)