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A149409 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, 0, 0), (-1, 0, 1), (0, -1, 1), (1, 0, 1), (1, 1, -1)} 0
1, 1, 4, 12, 52, 197, 847, 3606, 15852, 70792, 319238, 1458059, 6712464, 31103382, 145188780, 680497081, 3206436620, 15163714935, 71961913140, 342618244047, 1635473805211, 7827051661123, 37540855568739, 180418046385308, 868696755339059, 4189558069863009, 20236887246198359, 97887835211194854 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149407 A149408 A125529 * A149410 A149411 A149412

Adjacent sequences:  A149406 A149407 A149408 * A149410 A149411 A149412

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 21 13:44 EDT 2021. Contains 348155 sequences. (Running on oeis4.)