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
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
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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
Comments