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A148052 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), (-1, 1, 0), (1, 0, 0)} 0
1, 1, 2, 3, 10, 20, 63, 133, 516, 1218, 4465, 10703, 44548, 113711, 450058, 1153535, 4996768, 13352786, 55352661, 147886291, 657261944, 1810272037, 7740475160, 21274221703, 96257801996, 270869293600, 1184198800343, 3322353778443, 15231848541136, 43555542439718, 193622102777095, 551782565099753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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, -1 + j, 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: A148049 A148050 A148051 * A148053 A148054 A148055

Adjacent sequences:  A148049 A148050 A148051 * A148053 A148054 A148055

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)