A149650 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, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 277, 1305, 5551, 26459, 117339, 564175, 2569541, 12423757, 57631629, 279785441, 1314805215, 6403579035, 30380380575, 148347638871, 708946177403, 3469106040755, 16674006366701, 81734383525829, 394662393972669, 1937465356348453, 9390425835596597, 46157868733303741, 224412725792613665

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149647 A149648 A149649 * A318376 A186364 A105451

Adjacent sequences: A149647 A149648 A149649 * A149651 A149652 A149653

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved