A149455 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, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 50, 182, 712, 2711, 10672, 41470, 164102, 644580, 2557808, 10108272, 40194806, 159440027, 634857536, 2524253822, 10061284624, 40067909864, 159820748482, 637157976526, 2542888042852, 10145529835268, 40507851460434, 161706752889040, 645859214596938, 2579323889200758

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A364907 A299699 A056275 * A105968 A149456 A149457

Adjacent sequences: A149452 A149453 A149454 * A149456 A149457 A149458

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved