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 A151357 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), (1, 0)}. 0

%I

%S 1,0,1,3,4,20,65,175,742,2604,9072,36960,139392,538824,2198625,

%T 8735727,35456850,146812952,604215326,2521642266,10617725768,

%U 44760668160,190357768328,813800295880,3490232753680,15055389124320,65193213272800,283254330047520,1235731377864960,5407996483238160

%N 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), (1, 0)}.

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

%F G.f.: Int(Int(2*hypergeom([3/4,5/4],[2],64*t^3*(t+1)/(1-4*t^2)^2)/(1-4*t^2)^(3/2),t),t)/t^2. - _Mark van Hoeij_, Aug 14 2014

%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, j, -1 + 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}]

%K nonn,walk

%O 0,4

%A _Manuel Kauers_, Nov 18 2008

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Last modified February 28 00:28 EST 2020. Contains 332319 sequences. (Running on oeis4.)