A150805 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, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 31, 133, 579, 2596, 11806, 54379, 252781, 1184050, 5579143, 26424624, 125674028, 599902518, 2872454761, 13791585310, 66375869050, 320130372489, 1546910655218, 7487566750599, 36298015251699, 176209696993704, 856502249778262, 4168047108725262, 20304922152203169, 99014510884348398

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A150802 A150803 A150804 * A150806 A150807 A150808

Adjacent sequences: A150802 A150803 A150804 * A150806 A150807 A150808

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved