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A149461 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, 1), (0, 1, -1), (1, 0, 1), (1, 1, -1)} 0
1, 1, 4, 13, 51, 195, 817, 3432, 14911, 65235, 290915, 1307274, 5937716, 27149739, 125023447, 578769694, 2693341575, 12586059554, 59046681200, 277963746827, 1312588575963, 6215451532217, 29507007004207, 140401812189147, 669478104046067, 3198467824446743, 15308052743597454, 73385800384796322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149460 A219579 A300122 * A056276 A144035 A056277

Adjacent sequences:  A149458 A149459 A149460 * A149462 A149463 A149464

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 18 00:01 EDT 2021. Contains 347489 sequences. (Running on oeis4.)