A148315 - OEIS

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A148315

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

1, 1, 2, 5, 14, 38, 124, 376, 1294, 4282, 15297, 53096, 196380, 703207, 2666168, 9803953, 37810371, 142047071, 555546878, 2121629955, 8397566784, 32502960555, 129911998351, 508624323397, 2049487856803, 8102493104535, 32878695403814, 131065339081490, 535106099908126, 2148557956847231

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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[i, 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, 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: A371606 A148314 A001011 * A331573 A141752 A291729

Adjacent sequences: A148312 A148313 A148314 * A148316 A148317 A148318

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved