A149974 - OEIS

A149974

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

1, 2, 5, 16, 56, 204, 786, 3128, 12711, 52785, 222949, 953417, 4126429, 18040639, 79526717, 353268588, 1579911721, 7107040619, 32142739964, 146077453326, 666745748346, 3055449082093, 14053347095902, 64853142654332, 300211980316997, 1393701718048020, 6487246904221268, 30270900624928157

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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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A191241 A052708 A149973 * A149975 A149976 A141201

Adjacent sequences: A149971 A149972 A149973 * A149975 A149976 A149977

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved