A149552 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (-1, 1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 57, 191, 855, 3145, 14487, 56053, 262737, 1051331, 4980261, 20405301, 97446293, 406337835, 1952898023, 8257524711, 39874911661, 170547958021, 826500403861, 3568852451755, 17344940632033, 75496152867403, 367811310598781, 1611803820065771, 7869040621716937, 34683587276347697

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149549 A149550 A149551 * A084136 A091147 A351072

Adjacent sequences: A149549 A149550 A149551 * A149553 A149554 A149555

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved