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Number of closed walks of length 2n at any of the nodes of degree 1 on the graph of the (7,4) Hamming code.
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%I #6 Jun 13 2015 00:51:39

%S 1,1,4,24,176,1376,10944,87424,699136,5592576,44739584,357914624,

%T 2863312896,22906494976,183251943424,1466015514624,11728124051456,

%U 93824992280576,750599937982464,6004799503335424,48038396025634816

%N Number of closed walks of length 2n at any of the nodes of degree 1 on the graph of the (7,4) Hamming code.

%C a(n+1)=8^n/3+2^(n+1)/3 with g.f. (1-6x)/(1-10x+16x^2) counts walks of length 2n+1 between adjacent nodes of degrees 1 and 4 on the graph of the (7,4) Hamming code.

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).

%F G.f.: (1-9x+10x^2)/(1-10x+16x^2); a(n)=8^(n-1)/3+2^(n)/3+5*0^n/8.

%Y Cf. A082412, A103333.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Jan 31 2005