|
Search: id:A123916
|
|
|
| A123916 |
|
Number of binary words whose (unique) decreasing Lyndon decomposition is into Lyndon words each with an odd number of 1's; EULER transform of A000048. |
|
+0
1
|
|
| 1, 1, 2, 3, 6, 10, 19, 34, 65, 120, 229, 432, 829, 1583, 3051, 5874, 11370, 22012, 42756, 83113, 161917, 315723, 616588, 1205232, 2358604, 4619485, 9055960, 17766086, 34880215, 68524486, 134707150, 264960828, 521449025
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
FORMULA
|
Prod_{n>=1} 1/(1-q^n)^A000048(n) = 1+sum_{n>=1} a(n) q^n
|
|
EXAMPLE
|
The binary words 1111, 1101, 1001, 0101, 0111, 0001 of length 4 decompose as 1*1*1*1, 1*1*01, 1*001, 01*01, 0111, 0001 and each subword has an odd number of 1's, therefore a(4)=6
|
|
CROSSREFS
|
Cf. A000048.
Sequence in context: A003237 A165920 A026021 this_sequence A000693 A054178 A005833
Adjacent sequences: A123913 A123914 A123915 this_sequence A123917 A123918 A123919
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 28 2006
|
|
|
Search completed in 0.002 seconds
|
