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A149956 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), (0, 1, 0), (1, 0, 0)} 0
1, 2, 5, 16, 52, 179, 657, 2445, 9340, 36701, 145628, 586312, 2398468, 9879421, 41072067, 172514552, 728279781, 3094286178, 13241783880, 56885626708, 245535890251, 1065461753201, 4637394881411, 20257808425487, 88856696223318, 390704372696703, 1722913681845064, 7622404131695837 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, 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] + 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: A148391 A337268 A148392 * A149957 A148393 A148394

Adjacent sequences:  A149953 A149954 A149955 * A149957 A149958 A149959

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.)