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A148377 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, 0, -1), (0, 0, 1), (1, -1, 1), (1, 1, -1)} 0
1, 1, 2, 5, 16, 46, 159, 536, 1934, 7003, 26466, 99651, 386911, 1511570, 5975390, 23858941, 96321883, 390396528, 1598094790, 6580849011, 27219861639, 113308413777, 474111950971, 1989920536156, 8395337106697, 35557146881876, 150994719386489, 643782850876503, 2753641930173152 (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, 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: A075887 A306504 A148376 * A163865 A148378 A148379

Adjacent sequences:  A148374 A148375 A148376 * A148378 A148379 A148380

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)