%I A151408
%S A151408 1,1,2,5,12,34,97,287,887,2761,8833,28635,93897,312257,1046368,3539825,
               12066283,41387197,
%T A151408 142887038,495828190,1729130445,6057385620,21303526484,75209346309,266413953357,
               946691896721,
%U A151408 3373935569795,12056675023892,43193395482458,155104308523072,558187652361721,
               2012940278579932
%N A151408 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, 0), (0, 1), (1, -1), (1, 0)}
%H A151408 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>.
%t A151408 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]]; Table[Sum[aux[0, k, n], {k, 
               0, n}], {n, 0, 25}]
%Y A151408 Sequence in context: A004114 A076864 A032292 this_sequence A121956 A131467 
               A000103
%Y A151408 Adjacent sequences: A151405 A151406 A151407 this_sequence A151409 A151410 
               A151411
%K A151408 nonn,walk
%O A151408 0,3
%A A151408 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008