A149747 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), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 79, 321, 1497, 6611, 31267, 142939, 683295, 3189011, 15358587, 72654977, 351786797, 1679905819, 8166596697, 39267480997, 191484682817, 925533860027, 4524414195813, 21957732601813, 107554022372481, 523676216690483, 2569348152664739, 12543177465406789, 61627639102069263, 301516113072994259

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + 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: A149744 A149745 A149746 * A149748 A151494 A307052

Adjacent sequences: A149744 A149745 A149746 * A149748 A149749 A149750

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved