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, 3458764513820540928

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.

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

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

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

From Elmo R. Oliveira, Mar 07 2026: (Start)

E.g.f.: (5 + 3*exp(8*x))/8.

For n > 0: a(n) = A083233(n)/2 = A270568(n)/4. (End)

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. A016945, A082412, A083233, A083713, A103334, A157176, A270568.

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

Sequence in context: A136325 A382892 A194888 * A037762 A037650 A037769

Adjacent sequences: A103330 A103331 A103332 * A103334 A103335 A103336

Keyword

easy,nonn

Author

Paul Barry, Jan 31 2005

Status

approved