A150268 - OEIS

A150268

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

1, 2, 6, 22, 89, 382, 1702, 7781, 36229, 170985, 815280, 3918288, 18949282, 92098505, 449432199, 2200447618, 10803036616, 53158537133, 262081270998, 1294220057191, 6400089819063, 31687261079330, 157048357040647, 779063981769830, 3867712897176363, 19214747051732096, 95516560740768620

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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, 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: A049123 A200753 A165544 * A369439 A165545 A306023

Adjacent sequences: A150265 A150266 A150267 * A150269 A150270 A150271

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved