|
Search: id:A151328
|
|
|
| A151328 |
|
Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)} |
|
+0
1
|
|
| 1, 3, 16, 84, 484, 2843, 17193, 105553, 657177, 4133074, 26217040, 167455754, 1075896508, 6947158172, 45052303360, 293263303568, 1915285138362, 12545294612032, 82387919461119, 542332725044387, 3577577193573774, 23645483214136620, 156556003183195069, 1038219939150227788, 6895261278418168211
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
|
|
MATHEMATICA
|
aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
|
|
CROSSREFS
|
Sequence in context: A026131 A026160 A025187 this_sequence A076279 A056369 A056360
Adjacent sequences: A151325 A151326 A151327 this_sequence A151329 A151330 A151331
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
|
|
Search completed in 0.002 seconds
|
