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A150898 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, 1), (0, 1, 0), (1, -1, 1), (1, 1, -1), (1, 1, 1)} 0
1, 2, 8, 34, 157, 740, 3559, 17279, 84560, 415909, 2053550, 10167290, 50445068, 250679582, 1247241773, 6211477817, 30957382262, 154379894612, 770234085562, 3844323126635, 19193341885245, 95849502655529, 478759938038077, 2391764922831018, 11950308222386767, 59715800638647240, 298428643759601008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150895 A150896 A150897 * A150899 A150900 A084207

Adjacent sequences:  A150895 A150896 A150897 * A150899 A150900 A150901

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 26 21:14 EDT 2022. Contains 354885 sequences. (Running on oeis4.)