A150331 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, -1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 22, 88, 335, 1400, 5748, 24663, 105721, 462559, 2031230, 9019371, 40236527, 180707876, 814986092, 3692530833, 16788729777, 76594103804, 350439481630, 1607655898836, 7392501722960, 34066718762304, 157294639529607, 727573123022953, 3370929793881863, 15641536974373111, 72679826589668373

Offset

0,2

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150329 A323681 A150330 * A150332 A150333 A057787

Adjacent sequences: A150328 A150329 A150330 * A150332 A150333 A150334

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved