A150750 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, 1), (-1, 1, -1), (0, 1, 1), (1, -1, 0), (1, 1, 1)}

1, 2, 8, 29, 127, 526, 2420, 10624, 49914, 226414, 1076960, 4987976, 23924425, 112344643, 542087643, 2571154955, 12461595847, 59550464104, 289620932455, 1392050985731, 6788905487071, 32780909125398, 160230657330042, 776576750273720, 3802994157929216, 18488348795133145, 90683976946526103

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A150747 A150748 A150749 * A150751 A150752 A150753

Adjacent sequences: A150747 A150748 A150749 * A150751 A150752 A150753

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved