A148591 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, 0), (-1, 0, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 57, 191, 631, 2153, 7593, 26985, 98071, 361345, 1338423, 5051312, 19068103, 73036222, 280693079, 1086439277, 4235355213, 16553722376, 65194738319, 257295232507, 1020928712938, 4064700477810, 16231276471048, 65088461541823, 261496712860419, 1054565027693888, 4261322146852943

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A148589 A148590 A363592 * A148592 A148593 A148594

Adjacent sequences: A148588 A148589 A148590 * A148592 A148593 A148594

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved