A150123 - OEIS

A150123

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

1, 2, 6, 20, 68, 250, 934, 3566, 13912, 54916, 219020, 883022, 3585810, 14649798, 60248906, 248939966, 1032848900, 4304004792, 17994933548, 75461738696, 317428584708, 1338576137314, 5657484903550, 23966588848258, 101724451527310, 432529598663988, 1842399690180958, 7859958501725832

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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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A360294 A150121 A150122 * A082679 A094854 A217782

Adjacent sequences: A150120 A150121 A150122 * A150124 A150125 A150126

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved