A150989 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, 0), (1, -1, 0), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 37, 167, 752, 3503, 16338, 77337, 367016, 1755693, 8417735, 40551629, 195740690, 947789781, 4596821237, 22343646643, 108754769594, 530209557941, 2587894918437, 12647093223479, 61866651654678, 302941530380327, 1484635126546032, 7281810707827661, 35741024226550076, 175548055081259277

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150986 A150987 A150988 * A150990 A150991 A150992

Adjacent sequences: A150986 A150987 A150988 * A150990 A150991 A150992

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved