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A148396 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, 1, 1), (0, 1, -1), (1, 0, -1), (1, 0, 0)} 0
1, 1, 2, 5, 16, 53, 194, 706, 2725, 10743, 42930, 176429, 736356, 3103055, 13254641, 57222484, 249217292, 1093491029, 4832787312, 21511601604, 96258301287, 432911365017, 1957187892005, 8886827390535, 40506590113021, 185330994400795, 850969255259770, 3919560505626379, 18105550077932420 (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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A127498 A149958 A148395 * A108521 A148397 A148398

Adjacent sequences:  A148393 A148394 A148395 * A148397 A148398 A148399

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 25 12:12 EDT 2022. Contains 356984 sequences. (Running on oeis4.)