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A103333 Number of closed walks on the graph of the (7,4) Hamming code.

%I A103333 #19 Sep 09 2018 02:21:29
%S A103333 1,3,24,192,1536,12288,98304,786432,6291456,50331648,402653184,
%T A103333 3221225472,25769803776,206158430208,1649267441664,13194139533312,
%U A103333 105553116266496,844424930131968,6755399441055744,54043195528445952,432345564227567616
%N A103333 Number of closed walks on the graph of the (7,4) Hamming code.
%C A103333 Counts closed walks of length 2n at the degree 3 node of the graph of the (7,4) Hamming code. With interpolated zeros, counts paths of length n at this node.
%C A103333 a(n+1) = A157176(A016945(n)). - _Reinhard Zumkeller_, Feb 24 2009
%C A103333 For n>0: a(n) = A083713(n) - A083713(n-1). - _Reinhard Zumkeller_, Feb 22 2010
%D A103333 David J.C. Mackay, Information Theory, Inference and Learning Algorithms, CUP, 2003, p. 19
%H A103333 Nathaniel Johnston, <a href="/A103333/b103333.txt">Table of n, a(n) for n = 0..500</a>
%H A103333 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).
%F A103333 G.f.: (1-5*x)/(1-8*x);
%F A103333 a(n) = (3*8^n + 5*0^n)/8.
%F A103333 a(n) = 8*a(n-1) for n > 0. - _Harvey P. Dale_, Mar 02 2012
%p A103333 seq((3*8^n+5*`if`(n=0,1,0))/8,n=0..20); # _Nathaniel Johnston_, Jun 26 2011
%t A103333 Join[{1},NestList[8#&,3,20]] (* _Harvey P. Dale_, Mar 02 2012 *)
%Y A103333 Cf. A082412, A103334.
%Y A103333 Cf. A000302, A004171. - _Vincenzo Librandi_, Jan 22 2009
%K A103333 easy,nonn
%O A103333 0,2
%A A103333 _Paul Barry_, Jan 31 2005