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A148772 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, 0), (-1, 0, 0), (0, 1, -1), (1, 0, 1)} 0
1, 1, 3, 8, 22, 80, 249, 856, 3192, 10985, 41536, 155873, 576077, 2259396, 8615836, 33421793, 132726991, 517346484, 2066304258, 8264179261, 32924752702, 133558734601, 538585757755, 2184648069875, 8935778946260, 36392678823475, 149505229709908, 615088054360448, 2530475475935471 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A148770 A189944 A148771 * A148773 A148774 A093537

Adjacent sequences:  A148769 A148770 A148771 * A148773 A148774 A148775

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 20 23:04 EDT 2021. Contains 347596 sequences. (Running on oeis4.)