A148388 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, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 16, 51, 175, 587, 2128, 7800, 29627, 112965, 437356, 1708992, 6786643, 27181584, 109870626, 446436891, 1826522803, 7521234588, 31168555884, 129805992237, 542972032376, 2280107924147, 9614642418922, 40701846220612, 172919505735539, 736924493782813, 3149528055432525

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[-1 + i, 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: A121651 A054660 A231296 * A148389 A108529 A268213

Adjacent sequences: A148385 A148386 A148387 * A148389 A148390 A148391

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved