

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)).  Reinhard Zumkeller, Feb 24 2009
For n>0: a(n) = A083713(n)  A083713(n1).  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.: (15*x)/(18*x);
a(n) = (3*8^n + 5*0^n)/8.
a(n) = 8*a(n1) 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



