A150420 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, 0), (1, -1, 1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}

1, 2, 7, 24, 95, 381, 1618, 6947, 30662, 136573, 618099, 2818128, 12981409, 60152326, 280713698, 1316221777, 6203507127, 29349414927, 139399848256, 664156567450, 3174024450836, 15207455409058, 73041930090888, 351566863640124, 1695586707912644, 8192282542679420, 39647874861987388, 192172115316412119

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, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150417 A150418 A150419 * A150421 A150422 A137952

Adjacent sequences: A150417 A150418 A150419 * A150421 A150422 A150423

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved