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A149460 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), (1, 1, -1), (1, 1, 0)} 0
1, 1, 4, 13, 50, 205, 866, 3749, 16632, 75039, 341961, 1576018, 7327168, 34283739, 161361590, 763453145, 3627427677, 17298560102, 82772495282, 397211322958, 1910994001127, 9215181362223, 44529823106164, 215576405905591, 1045404537941408, 5077352560496235, 24694338511964747, 120257935938127480 (list; graph; refs; listen; history; text; internal format)
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, k, -1 + n] + aux[-1 + i, -1 + 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: A149458 A002746 A149459 * A219579 A300122 A149461

Adjacent sequences:  A149457 A149458 A149459 * A149461 A149462 A149463

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 18 03:30 EDT 2022. Contains 353783 sequences. (Running on oeis4.)