

A059222


Minimal number of disjoint edgepaths into which the graph of the nary cube can be partitioned.


3



1, 1, 4, 1, 16, 1, 64, 1, 256, 1, 1024, 1, 4096, 1, 16384, 1, 65536, 1, 262144, 1, 1048576, 1, 4194304, 1, 16777216, 1, 67108864, 1, 268435456, 1, 1073741824, 1, 4294967296, 1, 17179869184, 1, 68719476736, 1, 274877906944, 1, 1099511627776, 1, 4398046511104
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OFFSET

1,3


COMMENTS

The formula for this sequence is easily derived from a generalization of Euler's famous "Eulerian Path" theorem (see Theorem 11.2.4 in p. 419 of the reference).


REFERENCES

R. A. Brualdi, Introductory Combinatorics, 3rd ed. PrenticeHall, 1999.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..400
Index entries for linear recurrences with constant coefficients, signature (0,5,0,4).


FORMULA

a(n) = 1 if n is even and 2^(n1) if n is odd.
G.f. x*(1x+x^2+4*x^3) / ( (x1)*(2*x+1)*(2*x1)*(1+x) ).  R. J. Mathar, Apr 25 2013


EXAMPLE

a(5)=16 because 2^(51)=16. Consequently, the minimal number of disjoint edgepaths into which the 5ary cube can be partitioned is 16.


MATHEMATICA

Table[If[EvenQ[n], 1, 2^(n1)], {n, 80}] (* or *) Riffle[2^(2Range[0, 50]), 1] (* Harvey P. Dale, Nov 02 2011 *)


CROSSREFS

Cf. A057979.
Sequence in context: A123382 A197653 A146160 * A117292 A062780 A262616
Adjacent sequences: A059219 A059220 A059221 * A059223 A059224 A059225


KEYWORD

nonn


AUTHOR

Felix Golderg (felixg(AT)tx.technion.ac.il), Jan 19 2001


EXTENSIONS

More terms from Harvey P. Dale, Nov 02 2011


STATUS

approved



