A226555 Numerators of row sums of the triangular enumeration of rational numbers A226314(n,k) / A054531(n,k), 1 <= k <= n.

1, 5, 4, 13, 7, 25, 10, 33, 17, 45, 16, 69, 19, 65, 38, 81, 25, 109, 28, 125, 55, 105, 34, 177, 53, 125, 68, 181, 43, 241, 46, 193, 89, 165, 100, 301, 55, 185, 106, 321, 61, 349, 64, 293, 167, 225, 70, 433, 109, 341, 140, 349, 79, 433, 162, 465, 157, 285, 88

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

.   n         A226314(n,k) / A054531(n,k), 1<=k<=n<=12           row sums
.  --   -------------------------------------------------------- --------
.   1:  1                                                           1
.   2:  1/2 2                                                       5/2
.   3:  1/3 2/3 3                                                   4
.   4:  1/4 3/2 3/4 4                                              13/2
.   5:  1/5 2/5 3/5 4/5 5                                           7
.   6:  1/6 4/3 5/2 5/3 5/6 6                                      25/2
.   7:  1/7 2/7 3/7 4/7 5/7 6/7 7                                  10
.   8:  1/8 5/4 3/8 7/2 5/8 7/4 7/8 8                              33/2
.   9:  1/9 2/9 7/3 4/9 5/9 8/3 7/9 8/9 9                          17
.  10:  1/10 6/5 3/10 7/5 9/2 8/5 7/10 9/5 9/10 10                 45/2
.  11:  1/11 2/11 3/11 4/11 5/11 6/11 7/11 8/11 9/11 10/11 11      16
.  12:  1/12 7/6 9/4 10/3 5/12 11/2 7/12 11/3 11/4 11/6 11/12 12   69/2 .

Prog

(Haskell)
import Data.Ratio ((%), numerator); import Data.Function (on)
a226555 n = numerator $ sum $
            zipWith ((%) `on` toInteger) (a226314_row n) (a054531_row n)

Crossrefs

Cf. A040001 (denominators).

Sequence in context: A189235 A019068 A215947 * A147685 A353151 A078930

Adjacent sequences: A226552 A226553 A226554 * A226556 A226557 A226558

Keyword

nonn,frac

Author

Reinhard Zumkeller, Jun 10 2013

Status

approved