Search: id:A151323
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%I A151323
%S A151323 1,3,14,67,342,1790,9580,52035,285990,1586298,8864676,49844238,281719164,
               1599314652,9113895960,
%T A151323 52109150691,298806189318,1717855010274,9898828072692,57158263594458,330662400729492,
%U A151323 1916134078427556,11120825740970088,64634042348169294,376139362185133404,
               2191569966890629380
%N A151323 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,
               0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), 
               (0, 1), (1, 0), (1, 1)}
%H A151323 M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter 
               plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</
               a>.
%H A151323 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted 
               Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</
               a>.
%F A151323 G.f. appears to be (((1+2*x)/(1-6*x))^(1/4)-1)/(2*x) [From Mark van Hoeij 
               (hoeij(AT)math.fsu.edu), Nov 20 2009]
%t A151323 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, j, -1 + n] + aux[1 
               + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], 
               {n, 0, 25}]
%Y A151323 Sequence in context: A034275 A151322 A002320 this_sequence A113140 A151324 
               A121185
%Y A151323 Adjacent sequences: A151320 A151321 A151322 this_sequence A151324 A151325 
               A151326
%K A151323 nonn,walk
%O A151323 0,2
%A A151323 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008

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