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A103333 Number of closed walks on the graph of the (7,4) Hamming code. 11
1, 3, 24, 192, 1536, 12288, 98304, 786432, 6291456, 50331648, 402653184, 3221225472, 25769803776, 206158430208, 1649267441664, 13194139533312, 105553116266496, 844424930131968, 6755399441055744, 54043195528445952, 432345564227567616 (list; graph; refs; listen; history; text; internal format)
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)). [From Reinhard Zumkeller, Feb 24 2009]

For n>0: a(n) = A083713(n) - A083713(n-1). [From 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. [From 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. [From 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

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Last modified February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)