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A148365 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)} 0
1, 1, 2, 5, 15, 49, 169, 600, 2182, 8068, 30230, 114477, 437205, 1681223, 6501377, 25258166, 98507415, 385422665, 1512133656, 5946328430, 23429717559, 92475097681, 365528889119, 1446682746541, 5732033020113, 22733572517586, 90239946160346, 358474301769052, 1424975523589483, 5667795213027392 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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[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: A272460 A149937 A149938 * A001892 A176025 A084082

Adjacent sequences:  A148362 A148363 A148364 * A148366 A148367 A148368

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 28 06:00 EST 2021. Contains 340490 sequences. (Running on oeis4.)