A148993 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, 0, 1), (-1, 1, 1), (0, -1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 33, 116, 457, 1779, 7298, 29951, 126547, 536414, 2314334, 10024915, 43931836, 193265395, 857130216, 3814642513, 17078057893, 76692933568, 345966606563, 1564863049001, 7103272404463, 32318852693883, 147466431488714, 674246612926443, 3090039771478300, 14186964701487388

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A184512 A148991 A148992 * A148994 A148995 A148996

Adjacent sequences: A148990 A148991 A148992 * A148994 A148995 A148996

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved