A150532 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), (1, -1, 1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 107, 446, 2025, 8918, 41505, 188590, 891481, 4132317, 19736049, 92739682, 446130229, 2117054831, 10238057437, 48942490538, 237635998597, 1142501947395, 5564792591019, 26875763432150, 131235800084951, 636150349671024, 3112827543186475, 15134893430082618, 74187481114027469

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, j, k, -1 + n] + aux[-1 + 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: A286761 A150530 A150531 * A074420 A005034 A350796

Adjacent sequences: A150529 A150530 A150531 * A150533 A150534 A150535

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved