A149296 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, 0, 0), (-1, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 11, 46, 153, 677, 2455, 11106, 42895, 198457, 791305, 3702406, 15165773, 71734282, 299266047, 1425366120, 6033876043, 28912348233, 123853219579, 596225571156, 2578099387973, 12458031648720, 54309706631855, 263290014989332, 1155465606500309, 5616411745913101, 24793271401695375

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, j, -1 + k, -1 + n] + aux[1 + i, 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: A149293 A149294 A149295 * A149297 A149298 A149299

Adjacent sequences: A149293 A149294 A149295 * A149297 A149298 A149299

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved