A150587 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), (1, -1, 1), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 26, 111, 481, 2193, 10085, 47474, 224803, 1077775, 5188995, 25162971, 122400320, 598066157, 2928994719, 14387003558, 70791737849, 349043371267, 1723298321968, 8520694758681, 42173897158555, 208968240347143, 1036272016990523, 5143060421505411, 25541878702607141, 126928214706858961

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + 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: A150585 A150586 A196709 * A001862 A150588 A150589

Adjacent sequences: A150584 A150585 A150586 * A150588 A150589 A150590

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved