A150906 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, -1), (1, -1, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 31, 141, 579, 2637, 11658, 53730, 245184, 1145615, 5316641, 25100260, 117875813, 560486938, 2655943749, 12697363185, 60572829215, 290883443805, 1394741066965, 6722843752887, 32366602118582, 156491245246286, 755964200592160, 3664456744630402, 17752096869897428, 86241013154934282

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A318124 A295264 A150905 * A150907 A150908 A150909

Adjacent sequences: A150903 A150904 A150905 * A150907 A150908 A150909

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved