A149414 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, 0, 0), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 12, 53, 177, 828, 3094, 14824, 58033, 281684, 1141169, 5586654, 23180041, 114064351, 481510517, 2378380394, 10178922398, 50407914795, 218056976919, 1081961659417, 4722055959715, 23463965963873, 103158013453456, 513166328831217, 2270192767159448, 11303062638778405, 50271038033668035

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A262745 A180381 A149413 * A053454 A149415 A149416

Adjacent sequences: A149411 A149412 A149413 * A149415 A149416 A149417

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved