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A150277 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, 1, 0), (0, 1, -1), (0, 1, 0), (1, 0, 1)} 0
1, 2, 6, 23, 89, 353, 1471, 6242, 26712, 116074, 510008, 2254425, 10033860, 44944615, 202217909, 913563797, 4143671773, 18855556442, 86046484485, 393738362852, 1806026193866, 8301731429786, 38236965932111, 176438461832407, 815503547632070, 3775140300273871, 17501159489385700, 81241736134010383 (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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A189043 A228392 A190910 * A150278 A150279 A150280

Adjacent sequences:  A150274 A150275 A150276 * A150278 A150279 A150280

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 30 02:48 EDT 2020. Contains 337432 sequences. (Running on oeis4.)