|
| |
|
|
A143282
|
|
Number of binary words of length n containing at least one subword 1001 and no subwords 10^{i}1 with i<2.
|
|
1
| |
|
|
0, 0, 0, 0, 1, 2, 3, 5, 9, 15, 24, 38, 60, 94, 146, 225, 345, 527, 802, 1216, 1838, 2771, 4168, 6256, 9372, 14016, 20929, 31208, 46476, 69133, 102726, 152494, 226171, 335169, 496320, 734440, 1086102, 1605187, 2371049, 3500522, 5165573, 7619251
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
FORMULA
| G.f.: x^4/((x^3+x-1)*(x^4+x-1)).
a(n) = A000930(n+2) - A003269(n+4).
|
|
|
EXAMPLE
| a(7) = 5 because 5 binary words of length 7 have at least one subword 1001 and no subwords 11 or 101: 0001001, 0010010, 0100100, 1001000, 1001001.
|
|
|
MAPLE
| a:= n-> (Matrix (7, (i, j)-> `if` (i=j-1, 1, `if` (i=7, [-1, 0, -1, 0, 1, -1, 2][j], 0)))^n. <<(0$6), 1>>)[3, 1]: seq (a(n), n=0..50);
|
|
|
CROSSREFS
| Cf. A000930, A003269, 2nd column of A143291.
Sequence in context: A205536 A074693 A147322 * A097083 A200047 A147877
Adjacent sequences: A143279 A143280 A143281 * A143283 A143284 A143285
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008
|
| |
|
|
