A150153 - OEIS

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A150153

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

1, 2, 6, 20, 74, 286, 1156, 4802, 20424, 88416, 388558, 1728154, 7766068, 35203756, 160780734, 739100904, 3417064694, 15877515930, 74106064750, 347262568828, 1633119402146, 7705187224014, 36460485042190, 172989825363820, 822769665651888, 3921997461962730, 18733952939668598, 89655251453676982

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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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150152 A107284 A211966 * A150154 A006850 A150155

Adjacent sequences: A150150 A150151 A150152 * A150154 A150155 A150156

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved