A150489 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), (0, 0, 1), (0, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 2, 7, 25, 100, 413, 1772, 7778, 34802, 157902, 724912, 3358969, 15684512, 73715790, 348356092, 1653929306, 7884490185, 37718871521, 181002026123, 870951972338, 4201026878221, 20307395603628, 98354769234056, 477193788512700, 2318890023793577, 11284682442069819, 54987869345463673, 268265213303245200

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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A150486 A150487 A150488 * A150490 A150491 A346814

Adjacent sequences: A150486 A150487 A150488 * A150490 A150491 A150492

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved