A151102 - OEIS

A151102

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

1, 3, 11, 43, 183, 804, 3593, 16403, 75914, 354170, 1665099, 7885983, 37532516, 179316553, 860227887, 4140471444, 19977956382, 96628135136, 468432058624, 2274938810486, 11065752663237, 53910840100157, 263005760557395, 1284565970851187, 6281059887543450, 30744235672382452, 150621365818561127

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151100 A063031 A151101 * A151103 A049189 A049163

Adjacent sequences: A151099 A151100 A151101 * A151103 A151104 A151105

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved