A150443 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, 1, -1), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 24, 102, 408, 1780, 7757, 34690, 156181, 714290, 3284745, 15233382, 71023292, 333095347, 1568553797, 7414909448, 35181429040, 167431337614, 798833158181, 3821411069783, 18320729388070, 88002183243400, 423509713884975, 2041556485188807, 9856228838965220, 47651583418203953, 230679383659481441

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, -1 + k, -1 + n] + aux[-1 + i, 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, 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: A150441 A150442 A352906 * A150444 A150445 A150446

Adjacent sequences: A150440 A150441 A150442 * A150444 A150445 A150446

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved