A150316 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, 1, -1), (-1, 1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 88, 307, 1373, 5156, 23757, 93219, 436802, 1764928, 8361824, 34513404, 164810322, 691394058, 3321137711, 14112642022, 68100605945, 292419142044, 1416190849181, 6133951316583, 29794512601288, 129997620164309, 632986280624799, 2779206446859016, 13560545542449322, 59864741413738210

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150313 A150314 A150315 * A150317 A150318 A150319

Adjacent sequences: A150313 A150314 A150315 * A150317 A150318 A150319

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved