A148490 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), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 6, 21, 75, 284, 1109, 4470, 18453, 77433, 329126, 1415834, 6149299, 26931302, 118780241, 527010199, 2350740211, 10534962936, 47408681317, 214136796301, 970426128408, 4410950701961, 20104046171859, 91856203336505, 420644431533937, 1930293373533896, 8874862002582146, 40875930281689623

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A247416 A105872 A304781 * A006612 A116769 A294817

Adjacent sequences: A148487 A148488 A148489 * A148491 A148492 A148493

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved