A150261 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, 0, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 22, 87, 360, 1539, 6656, 29519, 131997, 599591, 2742867, 12663920, 58792883, 274700270, 1288694040, 6076057801, 28734777315, 136432700264, 649355428719, 3100237524391, 14831679544010, 71131351004963, 341724857266355, 1645043242447743, 7930615784450314, 38298338467995971, 185178317686261648

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A164651 A279566 A367413 * A308409 A150262 A101043

Adjacent sequences: A150258 A150259 A150260 * A150262 A150263 A150264

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved