A150879 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, 1), (0, -1, 1), (0, 1, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 8, 33, 148, 681, 3201, 15277, 73616, 357316, 1744329, 8549549, 42045074, 207306429, 1024243596, 5069175930, 25123000907, 124653578501, 619096123727, 3077246250728, 15306139934563, 76177126601999, 379317092707415, 1889599971716845, 9416765382945067, 46943668153619544, 234087406436239003

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150876 A150877 A150878 * A150880 A150881 A053817

Adjacent sequences: A150876 A150877 A150878 * A150880 A150881 A150882

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved