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A151424 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 0), (1, 1)}. 0

%I #7 Mar 25 2023 22:38:12

%S 1,5,58,864,14532,262644,4977800,97575176,1961361993,40200713991,

%T 836868065805,17643727208475,375932890593208,8081825426016234,

%U 175078871453866363,3818046005021353980,83747799012137460437,1846442940744222053799,40896246043951637989485,909514786452244849526786

%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 2 n steps taken from {(-1, -1), (-1, 0), (-1, 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[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]

%K nonn,walk

%O 0,2

%A _Manuel Kauers_, Nov 18 2008

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)