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URL: https://oeis.org/A151337

⇱ A151337 - OEIS

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A151337
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), (-1, 1), (0, 1), (1, -1)}.
0
1, 0, 0, 1, 2, 1, 11, 27, 60, 216, 724, 1976, 7140, 23723, 78257, 273707, 965000, 3354664, 12105626, 43619606, 158328834, 581558532, 2150453882, 7986765356, 29926146152, 112632743114, 426211686362, 1621337531160, 6195825999752, 23775419983051, 91628399336871, 354427790698043, 1375944479482008, 5359864838951956
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 31, Tag 36.
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, -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: A111724 A184299 A080371 * A013019 A012904 A013015
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved