A149222 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, -1), (-1, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 44, 142, 648, 2346, 10929, 41996, 198400, 790809, 3772937, 15423184, 74122058, 308698810, 1491917931, 6303461720, 30598038823, 130770863783, 636981609747, 2748036278509, 13422579735590, 58363260029680, 285708746598083, 1250618636818368, 6133514881151521, 27002871070397109

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, 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, 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: A332233 A149220 A149221 * A264571 A149223 A149224

Adjacent sequences: A149219 A149220 A149221 * A149223 A149224 A149225

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved