• Als Spam markieren
• Beitrag melden

• 
  Diese Gruppe Alles

• Archiv
• RSS-Feeds

• Kontakt
• Hilfe
• Impressum
• Datenschutz

Formula sought (enumerative combinatorics)

Formula sought

For the below input parameters v and k, v>=k,
what would be the equation that gives b ?

FYI: these parameters and results are integer values
from the field of enumerative combinatorics.
The b below is the result of a complete enumeration
for the given v,k.
What is needed is to know in advance how much b will be
for the given v,k without enumerating the whole set.
Can one formulate an equation for this?

v  k           b
-----------------
1  1           1
2  1           2
3  1           3

2  2           1
3  2           4
4  2           9
5  2          16

3  3           1
4  3           9
5  3          28
6  3          65
7  3         126

4  4           1
5  4          21
6  4          90
7  4         268
8  4         640
9  4        1314

5  5           1
6  5          52
7  5         298
8  5        1123
9  5        3278
10  5        7995
11  5       17104

6  6           1
7  6         136
8  6        1016
9  6        4783
10  6       16941
11  6       48895
12  6      121171
13  6      267369

7  7           1
8  7         379
9  7        3575
10  7       20720
11  7       88393
12  7      300683
13  7      861325
14  7     2160889
15  7     4884281

8  8           1
9  8        1126
10  8       13023
11  8       91412
12  8      465938
13  8     1860121
14  8     6144894
15  8    17505487
16  8    44343520
17  8   102177477

...

Antworten