A150884 - OEIS

A150884

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

1, 2, 8, 33, 150, 684, 3229, 15298, 73626, 355375, 1729522, 8436439, 41348599, 203019209, 999765220, 4930173250, 24359727084, 120490798599, 596787779737, 2958395511129, 14679546022648, 72889010886540, 362178959182390, 1800603552325418, 8956750649823073, 44572886772095708, 221909515125736005

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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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A053817 A150882 A150883 * A150885 A150886 A150887

Adjacent sequences: A150881 A150882 A150883 * A150885 A150886 A150887

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved