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A151465 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, 1)}. 0
1, 1, 5, 16, 69, 288, 1294, 5863, 27428, 129525, 622671, 3017788, 14788994, 72961131, 362686254, 1812678169, 9109932551, 45985005522, 233114127299, 1185997243463, 6054487301033, 31000477950556, 159174362867546, 819349202675383, 4227486665984523, 21858721760539178, 113248919676873452 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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[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[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A220903 A042087 A332470 * A363299 A151474 A138550
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 17 05:50 EDT 2024. Contains 374360 sequences. (Running on oeis4.)