A148547 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), (-1, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 5, 19, 51, 179, 537, 2047, 6877, 26069, 89565, 357789, 1308757, 5195025, 19133803, 78842569, 301895385, 1236230249, 4740891949, 19969111093, 78741281045, 329548045841, 1298414880173, 5557411276513, 22373769659021, 95144521214133, 382311653159411, 1656255951338899, 6773128550423957

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[1 + 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: A340737 A209778 A148546 * A360086 A127998 A174132

Adjacent sequences: A148544 A148545 A148546 * A148548 A148549 A148550

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved