A149745 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, 0, 0), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 79, 321, 1495, 6571, 31009, 141345, 674375, 3141567, 15106187, 71367081, 345115645, 1646406573, 7995517313, 38414709245, 187167554711, 904086623973, 4416440135227, 21422272614469, 104868344343987, 510368704208833, 2502772503138939, 12213419014320941, 59980856399588001, 293360073380340249

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, 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: A009234 A211474 A149744 * A149746 A149747 A149748

Adjacent sequences: A149742 A149743 A149744 * A149746 A149747 A149748

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved