A150479 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, 0, 1), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 100, 398, 1652, 6956, 29787, 128925, 563042, 2478992, 10987489, 48981786, 219416367, 987118004, 4458156696, 20203631329, 91841898320, 418644067776, 1913128048163, 8762818322115, 40221642374777, 184976329216192, 852212015882142, 3932780978049604, 18176976409015648, 84133167344160970

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A151537 A074421 A150478 * A150480 A150481 A150482

Adjacent sequences: A150476 A150477 A150478 * A150480 A150481 A150482

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved