A244734 - OEIS

%I #18 Jul 30 2014 05:39:41

%S 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,

%T 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,

%U 11,56,57,58,59,12,61,62,63,64,13,6,67,34,23,35,71,12,73,37,25,38,7,13

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

%C The rational triangle T(n,k) begins:

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

%C 0:   1

%C 1:   2   3/2

%C 2:   4   5/2   2

%C 3:   7    4    3   5/2

%C 4:  11    6  13/3  7/2    3

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

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

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

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

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

%C ... reformatted and formula corrected. - _Wolfdieter Lang_, Jul 28 2014

%F a(n,k) = numerator((n*(n+1)/2+k+1)/(k+1)), n >= k >= 0. -_Wolfdieter Lang_, Jul 28 2014

%e The triangle a(n,k) begins:

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

%e 0:    1

%e 1:    2   3

%e 2:    4   5   2

%e 3:    7   4   3   5

%e 4:   11   6  13   7   3

%e 5:   16  17   6  19   4   7

%e 6:   22  23   8  25  26   9   4

%e 7:   29  15  31   8  33  17   5   9

%e 8:   37  19  13  10  41   7  43  11  5

%e 9:   46  47  16  49  10  17  52  53  6  11

%e ... reformatted - _Wolfdieter Lang_, Jul 28 2014

%e First column: A000124. Main diagonal: A145051 from A026741.

%e Alternate main and second diagonal: in A173234.

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

%Y Cf. A244840 (denominators).

%K nonn,tabl,easy

%O 0,2

%A _Paul Curtz_, Jul 05 2014

%E 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