A149371 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, 0), (1, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 46, 161, 679, 2679, 11335, 46123, 202969, 861581, 3802695, 16362599, 73645207, 323694943, 1459832206, 6466787674, 29501513081, 132348273267, 604673867966, 2726426138913, 12550493380399, 57060735346881, 262973859896489, 1199843537998945, 5558950506623078, 25511445519043023

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A166115 A027288 A149370 * A149372 A126202 A149373

Adjacent sequences: A149368 A149369 A149370 * A149372 A149373 A149374

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved