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A149425 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), (0, -1, 0), (0, 1, -1), (1, 1, 1)}. 0
1, 1, 4, 13, 42, 146, 520, 1893, 6928, 25520, 95258, 357332, 1348314, 5109674, 19419422, 74124571, 283750244, 1089053340, 4189218564, 16143369610, 62342218516, 241154261642, 934254937426, 3624326380994, 14076738707662, 54742699821140, 213116870712502, 830503102890218, 3239368922556944 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A082989 A267240 A192802 * A047144 A072307 A266494

Adjacent sequences:  A149422 A149423 A149424 * A149426 A149427 A149428

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 2 23:30 EST 2021. Contains 349445 sequences. (Running on oeis4.)