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A059222 Minimal number of disjoint edge-paths into which the graph of the n-ary 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 (list; graph; refs; listen; history; text; internal format)
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. Prentice-Hall, 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^(n-1) if n is odd.

G.f. -x*(-1-x+x^2+4*x^3) / ( (x-1)*(2*x+1)*(2*x-1)*(1+x) ). - R. J. Mathar, Apr 25 2013

EXAMPLE

a(5)=16 because 2^(5-1)=16. Consequently, the minimal number of disjoint edge-paths into which the 5-ary cube can be partitioned is 16.

MATHEMATICA

Table[If[EvenQ[n], 1, 2^(n-1)], {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

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)