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A151336 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, -1)}. 0
1, 0, 0, 1, 2, 0, 5, 26, 28, 42, 369, 908, 1122, 5773, 23119, 42716, 117508, 549438, 1479612, 3367843, 13480787, 46542736, 115686395, 371629486, 1402498101, 4078027887, 11785376915, 42758254550, 140673861443, 410211643221, 1373805039590, 4780700411490, 14793100980164, 47088191339857, 163599002479471 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 10, Tag 14.
M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
MATHEMATICA
aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
CROSSREFS
Sequence in context: A263101 A219765 A153059 * A346092 A180491 A329893
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)