A149920 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, 0), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 47, 157, 556, 2019, 7584, 29152, 113984, 453620, 1829076, 7459678, 30755525, 127897631, 536170959, 2264041183, 9619849541, 41113706454, 176630946692, 762409276043, 3305293076682, 14386354109668, 62846284893256, 275475587203370, 1211274147573245, 5341553425781988

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149918 A353028 A149919 * A149921 A149922 A192053

Adjacent sequences: A149917 A149918 A149919 * A149921 A149922 A149923

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved