A151068 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), (0, 0, -1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 10, 39, 161, 677, 2928, 12960, 58017, 262405, 1199539, 5525169, 25596413, 119257971, 558421159, 2625162125, 12385172472, 58627444543, 278328330444, 1324693681144, 6319734719386, 30214893750138, 144737543240666, 694559665936562, 3338525853202416, 16071560266421005, 77475630137792744

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A296195 A123768 A005750 * A151069 A151070 A151071

Adjacent sequences: A151065 A151066 A151067 * A151069 A151070 A151071

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved