A150548 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, 1), (-1, 1, 0), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 105, 431, 1827, 7883, 34355, 151327, 672562, 3005578, 13506779, 60999340, 276513218, 1257747158, 5739244040, 26258189734, 120423829974, 553516970829, 2549217000255, 11761428696128, 54355208008882, 251586124907058, 1166116972610051, 5412142000435618, 25149404570126040, 116998424278050487

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A151296 A141370 A150547 * A150549 A150550 A150551

Adjacent sequences: A150545 A150546 A150547 * A150549 A150550 A150551

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved