A149577 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), (0, 0, -1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 51, 199, 755, 2821, 11457, 45421, 180609, 740097, 3026837, 12362553, 51258493, 213094839, 885144315, 3704575695, 15563367115, 65372995019, 275716820519, 1166762781235, 4940175457887, 20965390531703, 89209748891747, 379961694898047, 1620676281126587, 6926567928761055

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A199985 A255442 A149576 * A149578 A149579 A149580

Adjacent sequences: A149574 A149575 A149576 * A149578 A149579 A149580

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved