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

1, 3, 24, 192, 1536, 12288, 98304, 786432, 6291456, 50331648, 402653184, 3221225472, 25769803776, 206158430208, 1649267441664, 13194139533312, 105553116266496, 844424930131968, 6755399441055744, 54043195528445952, 432345564227567616

Offset: 0

Author

Paul Barry, Jan 31 2005

Keywords

• easy
• nonn

Comments

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.

a(n+1) = A157176(A016945(n)). - Reinhard Zumkeller, Feb 24 2009

For n>0: a(n) = A083713(n) - A083713(n-1). - Reinhard Zumkeller, Feb 22 2010

References

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (8).

Crossrefs

Cf. A082412, A103334.

Cf. A000302, A004171. - Vincenzo Librandi, Jan 22 2009

Programs

Maple

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

Mathematica

Join[{1},NestList[8#&,3,20]] (* Harvey P. Dale, Mar 02 2012 *)

Formula

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

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

a(n) = 8*a(n-1) for n > 0. - Harvey P. Dale, Mar 02 2012