A149440 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, 0), (0, -1, 1), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 4, 13, 47, 178, 717, 2931, 12206, 51725, 222382, 965695, 4229004, 18663791, 82908381, 370362024, 1662456328, 7494619832, 33916523818, 154011480462, 701493894387, 3204032461602, 14671001493623, 67330937214095, 309654418218959, 1426834603648238, 6586249762098228, 30451755568889279

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A017945 A055451 A163862 * A149441 A149442 A078468

Adjacent sequences: A149437 A149438 A149439 * A149441 A149442 A149443

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved