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A151479 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, 1), (0, -1), (0, 1), (1, 0), (1, 1)}. 0

%I #7 Jan 01 2024 02:35:45

%S 1,1,5,17,77,345,1649,8081,40603,207911,1080842,5691069,30285103,

%T 162630700,880180326,4796131934,26290963023,144882598329,802180091860,

%U 4460270007514,24894507295247,139425927499075,783332991179825,4413617609260839,24933618943094571,141197619861619694,801383347755022792

%N 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, 1), (0, -1), (0, 1), (1, 0), (1, 1)}.

%H M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</a>.

%t 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[-1 + i, 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, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

%K nonn,walk

%O 0,3

%A _Manuel Kauers_, Nov 18 2008

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Last modified April 21 23:54 EDT 2024. Contains 371886 sequences. (Running on oeis4.)