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A148042 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, 1), (-1, 1, 0), (0, 1, -1), (1, 0, 0), (1, 1, -1)} 0
1, 1, 2, 3, 8, 19, 57, 165, 535, 1700, 5761, 19596, 69357, 247143, 904969, 3344222, 12578803, 47771691, 183784047, 713153652, 2795057882, 11038817438, 43945343994, 176118626035, 710510882943, 2883088313211, 11764647473938, 48250711908615, 198849105981280, 823144145532963, 3421816206647552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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, 1 + k, -1 + n] + aux[-1 + i, 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, -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: A148039 A148040 A148041 * A077269 A294431 A148043

Adjacent sequences:  A148039 A148040 A148041 * A148043 A148044 A148045

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)