A148477 - OEIS

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A148477

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

1, 1, 2, 6, 20, 67, 253, 957, 3841, 15474, 64472, 269779, 1152812, 4946845, 21526634, 94037657, 414827211, 1836302134, 8186401788, 36608956495, 164582568876, 741942696193, 3358416244905, 15238713101124, 69369936227451, 316460578849534, 1447475542934734, 6633146638804745, 30463119151349776

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, j, -1 + 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: A372872 A148475 A148476 * A369123 A027063 A291005

Adjacent sequences: A148474 A148475 A148476 * A148478 A148479 A148480

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved