A150370 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, 1, 0), (1, 0, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 23, 94, 366, 1572, 6510, 29057, 126170, 573577, 2550329, 11787602, 53536730, 249807454, 1148715115, 5408943850, 25167049884, 119194478064, 558795070017, 2661662539254, 12570487465818, 60111542243799, 285330289292712, 1369765721169165, 6534443286670410, 31458470097759095, 150612341370229637

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150367 A150368 A150369 * A150371 A150372 A150373

Adjacent sequences: A150367 A150368 A150369 * A150371 A150372 A150373

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved