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

0,2

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).

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

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 *)

Crossrefs

Cf. A082412, A103334.

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

Sequence in context: A122741 A136325 A194888 * A037762 A037650 A037769

Adjacent sequences: A103330 A103331 A103332 * A103334 A103335 A103336

Keyword

easy,nonn

Author

Paul Barry, Jan 31 2005

Status

approved