|
Search: id:A078807
|
|
|
| A078807 |
|
Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd, and first letter 0. |
|
+0
3
|
|
| 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2, 1, 1, 3, 3, 3, 2, 1, 0, 0, 1, 3, 4, 5, 4, 3, 1, 1, 4, 6, 7, 7, 5, 3, 1, 0, 0, 1, 4, 7, 10, 11, 10, 7, 4, 1, 1, 5, 10, 14, 17, 16, 13, 8, 4, 1, 0, 0, 1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1, 1, 6, 15, 25, 35, 40, 39, 32, 22, 12, 5, 1, 0, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
0,13
|
|
|
COMMENT
|
Row sums: 0,1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045).
|
|
REFERENCES
|
Clark Kimberling, Binary Words with Restricted Repetitions and Associated Compositions of Integers, preprint.
|
|
FORMULA
|
T(n, k)=T(n-1, n-k-1)+T(n-3, n-k-3)+...+T(n-2m-1, n-k-2m-1), where m=[(n-1)/2], and (by definition) T(i, j)=0 if i<0 or j<0 or i=j.
|
|
EXAMPLE
|
T(6,2) counts the words 010001 and 000101. Top of triangle:
0 = T(0,0)
1 = T(1,0)
0 1 = T(2,0) T(2,1)
1 1 0
0 1 1 1
1 2 1 1 0
|
|
CROSSREFS
|
Cf. A078808, A078821.
Sequence in context: A093829 A113447 A137608 this_sequence A029422 A117452 A029412
Adjacent sequences: A078804 A078805 A078806 this_sequence A078808 A078809 A078810
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Dec 07 2002
|
|
|
Search completed in 0.002 seconds
|
