%I A151415
%S A151415 1,0,2,3,10,27,89,267,868,2858,9510,31830,108638,373219,1288064,4482534,
               15710368,55258931,
%T A151415 195240700,693284513,2470263132,8827776270,31654190580,113835950410,410335021648,
               1482638356348,
%U A151415 5369592056146,19484896375080,70835100481126,257981797359638,941120763934455,
               3438343699103345
%N A151415 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), (0, -1), (1, 0), (1, 1)}
%H A151415 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 A151415 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[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, n], 
               {k, 0, n}], {n, 0, 25}]
%Y A151415 Sequence in context: A005158 A005225 A052929 this_sequence A134588 A000060 
               A089752
%Y A151415 Adjacent sequences: A151412 A151413 A151414 this_sequence A151416 A151417 
               A151418
%K A151415 nonn,walk
%O A151415 0,3
%A A151415 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008