A149380 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, 0), (0, -1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 12, 48, 175, 720, 2926, 12453, 53326, 233271, 1029702, 4600541, 20713662, 94035765, 429502102, 1973663417, 9113809036, 42279636026, 196921587757, 920531411848, 4317237141695, 20307973562835, 95786786404463, 452923752976475, 2146518741145518, 10194348350275765, 48509687121572291

Offset

0,3

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A063887 A149378 A149379 * A149381 A149382 A149383

Adjacent sequences: A149377 A149378 A149379 * A149381 A149382 A149383

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved