|
| |
|
|
A005222
|
|
Number of Dyck paths of knight moves.
(Formerly M3234)
|
|
0
| |
|
|
1, 0, 1, 0, 4, 4, 18, 26, 86, 158, 462, 976, 2665, 6082, 16040, 38338, 99536, 244880, 631923, 1583796, 4081939, 10358670, 26728731, 68425494, 176964795, 455967376, 1182454137, 3061954102, 7962768190, 20702327552, 53983118006, 140817757006
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
REFERENCES
| J. Labelle and Y.-N. Yeh, Dyck paths of knight moves, Discrete Applied Math., 24 (1989), 213-221.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| G.f.: A+z^4A^3/(1-zA)^2, where A=(1+2z+sqrt(1-4z+4z^2-4z^4)-sqrt(2)*sqrt(1-4z^2-2z^4+(2z+1)sqrt(1-4z+4z^2-4z^4)))/[4z^2].
|
|
|
CROSSREFS
| Sequence in context: A086448 A128090 A119948 * A133039 A177117 A035413
Adjacent sequences: A005219 A005220 A005221 * A005223 A005224 A005225
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 17 2003
|
| |
|
|
