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A149939 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, -1), (-1, 1, 1), (0, 0, 1), (1, 0, 0)} 0
1, 2, 5, 15, 49, 170, 619, 2302, 8723, 33708, 132118, 524213, 2099108, 8469819, 34428721, 140827947, 579195024, 2393319428, 9930326669, 41361965397, 172876964154, 724796212419, 3047269940521, 12844242301182, 54266727185459, 229774872053471, 974848465781183, 4143560333822301 (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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A176025 A084082 A190270 * A149940 A149941 A149942

Adjacent sequences:  A149936 A149937 A149938 * A149940 A149941 A149942

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 5 17:29 EDT 2020. Contains 335473 sequences. (Running on oeis4.)