A149828 - OEIS

A149828

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), (0, 0, 1), (1, -1, 0), (1, 0, 0)}.

1, 2, 4, 10, 28, 85, 282, 947, 3278, 11804, 42992, 160394, 608956, 2332267, 9090053, 35744068, 141703215, 568391420, 2292523599, 9317832473, 38156420126, 156926908434, 649714165554, 2703041451296, 11290430424568, 47410223465862, 199762347764634, 844895895804548, 3587763601824528

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OFFSET

0,2

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, j, k, -1 + n] + aux[-1 + i, 1 + 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, 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: A149825 A149826 A149827 * A149829 A149830 A272484

Adjacent sequences: A149825 A149826 A149827 * A149829 A149830 A149831

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved