A149839 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), (-1, 0, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 4, 12, 36, 105, 359, 1206, 4067, 14822, 52823, 192009, 724475, 2688197, 10212299, 39371249, 150595178, 587964607, 2302876044, 9017714047, 35830596795, 142208608418, 566950728006, 2279733680236, 9155169681193, 36992776831504, 150085692169723, 609053481684281, 2485541205785126

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[i, -1 + j, k, -1 + n] + aux[1 + 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: A149837 A149838 A192236 * A149840 A224540 A025579

Adjacent sequences: A149836 A149837 A149838 * A149840 A149841 A149842

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved