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A103333 Number of closed walks on the graph of the (7,4) Hamming code. 11

%I

%S 1,3,24,192,1536,12288,98304,786432,6291456,50331648,402653184,

%T 3221225472,25769803776,206158430208,1649267441664,13194139533312,

%U 105553116266496,844424930131968,6755399441055744,54043195528445952,432345564227567616

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

%C 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 a(n+1) = A157176(A016945(n)). - _Reinhard Zumkeller_, Feb 24 2009

%C For n>0: a(n) = A083713(n) - A083713(n-1). - _Reinhard Zumkeller_, Feb 22 2010

%D David J.C. Mackay, Information Theory, Inference and Learning Algorithms, CUP, 2003, p. 19

%H Nathaniel Johnston, <a href="/A103333/b103333.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).

%F G.f.: (1-5*x)/(1-8*x);

%F a(n) = (3*8^n + 5*0^n)/8.

%F a(n) = 8*a(n-1) for n > 0. - _Harvey P. Dale_, Mar 02 2012

%p seq((3*8^n+5*`if`(n=0,1,0))/8,n=0..20); # _Nathaniel Johnston_, Jun 26 2011

%t Join[{1},NestList[8#&,3,20]] (* _Harvey P. Dale_, Mar 02 2012 *)

%Y Cf. A082412, A103334.

%Y Cf. A000302, A004171. - _Vincenzo Librandi_, Jan 22 2009

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 31 2005

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)