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A151043 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, -1), (0, 0, 1), (0, 1, 1), (1, 0, 0)} 0
1, 3, 9, 33, 129, 516, 2150, 9087, 38998, 169860, 745294, 3299632, 14710027, 65916647, 296959414, 1343326744, 6099110908, 27786718053, 126954339999, 581583216022, 2670632483217, 12289630867712, 56665692946039, 261744829070297, 1211008003679833, 5611462558701255, 26038256666321760, 120979359155524014 (list; graph; refs; listen; history; text; internal format)
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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A151042 A087289 A084508 * A151044 A247195 A236408

Adjacent sequences:  A151040 A151041 A151042 * A151044 A151045 A151046

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 3 10:43 EDT 2021. Contains 346435 sequences. (Running on oeis4.)