Search: id:A151162
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%I A151162
%S A151162 1,3,12,45,180,702,2808,11097,44388,176418,705672,2812482,11249928,44903484,
               179613936,
%T A151162 717517521,2870070084,11470898106,45883592424,183438670950,733754683800,
               2934026948196,
%U A151162 11736107792784,46934017407594,187736069630376,750833732416212,3003334929664848
%N A151162 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,
               0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 
               0, 1), (1, 1, 0)}
%C A151162 Hankel transform is 3^C(n+1,2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 01 2009]
%C A151162 Inverse binomial transform of A151253 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 03 2009]
%H A151162 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 A151162 a(n)=sum{k=0..n, A120730(n,k)*3^k}. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 01 2009]
%F A151162 a(2n+2)=4*a(2n+1), a(2n+1)=4*a(2n)-3^n*A000108(n)=4*a(2n)-A005159(n). 
               G.f.:(sqrt(1-12*x^2)+6x-1)/(6x*(1-4x)). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 02 2009]
%t A151162 aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, 
               n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], 
               True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + 
               i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, 
               k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 
               0, n}], {n, 0, 10}]
%Y A151162 Sequence in context: A085481 A030195 A114515 this_sequence A094547 A026559 
               A008781
%Y A151162 Adjacent sequences: A151159 A151160 A151161 this_sequence A151163 A151164 
               A151165
%K A151162 nonn,walk
%O A151162 0,2
%A A151162 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008

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