A151000 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, 0, 1), (0, 1, -1), (0, 1, 1), (1, -1, 0), (1, 1, 1)}.

1, 2, 9, 38, 174, 809, 3844, 18453, 89381, 435538, 2132335, 10476821, 51621051, 254914718, 1261096981, 6248016875, 30993074650, 153896056649, 764821193488, 3803687896469, 18928494638048, 94244360957085, 469451989760545, 2339360937296214, 11661420918757803, 58148064857949913, 290023251544762577

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150997 A150998 A150999 * A151001 A151002 A151003

Adjacent sequences: A150997 A150998 A150999 * A151001 A151002 A151003

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved