A150400 - OEIS

A150400

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

1, 2, 7, 24, 92, 367, 1532, 6537, 28401, 125402, 561269, 2538592, 11577377, 53180725, 245851609, 1142923676, 5338638677, 25039506213, 117875420742, 556766876129, 2637704680575, 12529671735438, 59662379461044, 284722182663471, 1361521325882578, 6522820677722090, 31303032186007578, 150459777222112891

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OFFSET

0,2

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, 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: A150397 A150398 A150399 * A150401 A003041 A026558

Adjacent sequences: A150397 A150398 A150399 * A150401 A150402 A150403

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved