A150644 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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 2, 7, 27, 118, 522, 2420, 11289, 53793, 257362, 1244961, 6039808, 29485738, 144258235, 708480043, 3485227388, 17187200327, 84865641756, 419743432518, 2078100373296, 10300559457528, 51096787670550, 253687974620399, 1260301870804674, 6265125287549723, 31160154012544656, 155054753225871295

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150641 A150642 A150643 * A007166 A036783 A368762

Adjacent sequences: A150641 A150642 A150643 * A150645 A150646 A150647

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved