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A149493 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), (-1, 1, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)} 0
1, 1, 4, 14, 60, 251, 1120, 5034, 23167, 107491, 504444, 2382474, 11326009, 54091015, 259422990, 1248388483, 6025296992, 29153344429, 141368541183, 686821433084, 3342472006964, 16290717857322, 79504766682773, 388478084327045, 1900247753858534, 9304229885789657, 45597320486134219, 223642198438153404 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, k, -1 + n] + aux[-1 + i, 1 + 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, 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: A307488 A241706 A111276 * A299926 A307399 A307411

Adjacent sequences:  A149490 A149491 A149492 * A149494 A149495 A149496

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 25 05:11 EST 2020. Contains 332217 sequences. (Running on oeis4.)