A150683 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), (-1, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 8, 26, 116, 428, 1998, 7846, 37336, 152208, 732226, 3060418, 14830916, 63105628, 307405454, 1325797950, 6483199136, 28258790888, 138595056794, 609285087066, 2995224031548, 13260539061908, 65311730280966, 290865915803798, 1434828620260472, 6422339118113504, 31722512524233362, 142611202226642162

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, -1 + 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, 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: A150681 A150682 A303478 * A150684 A150685 A150686

Adjacent sequences: A150680 A150681 A150682 * A150684 A150685 A150686

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved