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A149414 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, 0, 0), (-1, 1, 1), (1, 0, 1), (1, 1, -1)}. 0
1, 1, 4, 12, 53, 177, 828, 3094, 14824, 58033, 281684, 1141169, 5586654, 23180041, 114064351, 481510517, 2378380394, 10178922398, 50407914795, 218056976919, 1081961659417, 4722055959715, 23463965963873, 103158013453456, 513166328831217, 2270192767159448, 11303062638778405, 50271038033668035 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A262745 A180381 A149413 * A053454 A149415 A149416
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 20 06:42 EDT 2024. Contains 371799 sequences. (Running on oeis4.)