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A149914 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, -1), (-1, -1, 1), (-1, 1, 0), (0, 1, 0), (1, 0, 0)} 0
1, 2, 5, 15, 47, 150, 511, 1818, 6553, 24152, 91011, 345464, 1323971, 5153325, 20242463, 79980418, 318692165, 1278021945, 5144043475, 20816623561, 84730346521, 346195467540, 1419588411167, 5844061918042, 24128251545872, 99868971598520, 414648751273051, 1726489726795012, 7204868556994227 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A058495 A287275 A151280 * A071735 A148363 A350434

Adjacent sequences:  A149911 A149912 A149913 * A149915 A149916 A149917

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 22 18:37 EST 2022. Contains 350488 sequences. (Running on oeis4.)