A149420 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, 1), (-1, 1, 0), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 56, 191, 919, 3461, 16942, 67024, 330985, 1351694, 6706020, 28005748, 139322499, 591548083, 2947755005, 12676627994, 63236396201, 274723412297, 1371393625593, 6007561120023, 30003252219169, 132346186373218, 661182403536292, 2933681027414591, 14659537853840122, 65373537954378185

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A151469 A268408 A092576 * A298680 A149421 A051195

Adjacent sequences: A149417 A149418 A149419 * A149421 A149422 A149423

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved