Search: id:A049037
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%I A049037
%S A049037 1,6,54,996,22734,577692,15680628,445162392,13055851998,392475442092,
%T A049037 12029082873372,374482032292008,11808861461931492,376406128925067528,
%U A049037 12108063535794336312,392560994063887113744,12814685828476778001726
%N A049037 Number of cubic lattice walks that start and end at origin after 2n steps, 
               not touching origin at intermediate stages.
%D A049037 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 322-331.
%H A049037 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/polya/flajolet.html">
               Symmetric Random Walk on n-Dimensional Integer Lattice</a>
%H A049037 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A049037 Define a_0, a_1, ... = [ 1, 6, 54, ... ] by 1+Sum b_i x^i = 1/(1-Sum 
               a_i x^i) where b_0, b_1, ... = [ 1, 6, 90, ... ] = A002896.
%F A049037 Or, Sum[ a(n) x^(2n), n=1, 2, ...infinity ] = 1-1/Sum[ A002896(n)*x^(2n), 
               n=0, 1, ...infinity ].
%e A049037 a(5)=577692 i.e. there are 577692 different walks that start and end 
               at origin after 2*5=10 steps, avoiding origin at intermediate steps.
%p A049037 read transforms; t1 := [ seq(A002896(i),i=1..25) ]; INVERTi(t1);
%Y A049037 Invert A002896.
%Y A049037 Sequence in context: A072034 A167571 A138434 this_sequence A047681 A075575 
               A073655
%Y A049037 Adjacent sequences: A049034 A049035 A049036 this_sequence A049038 A049039 
               A049040
%K A049037 easy,nonn,nice
%O A049037 0,2
%A A049037 Alessandro Zinani (alzinani(AT)tin.it)

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