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A148489 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, 0), (-1, 1, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 6, 21, 73, 272, 1055, 4226, 17296, 72002, 304223, 1302487, 5631257, 24557910, 107912037, 477269006, 2122877159, 9489677428, 42608326043, 192070741414, 868890650080, 3943246247910, 17947364156580, 81901112293463, 374647230094154, 1717560685555588, 7890073413521769, 36312976830040510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A047106 A148487 A148488 * A116771 A294765 A116745

Adjacent sequences:  A148486 A148487 A148488 * A148490 A148491 A148492

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 1 10:38 EDT 2022. Contains 354969 sequences. (Running on oeis4.)