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
E.g.f.: cosh(x)*(1 + sinh(x)) - 1. - Stefano Spezia, Mar 26 2022
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
KEYWORD
nonn,easy
AUTHOR
Felix Golderg (felixg(AT)tx.technion.ac.il), Jan 19 2001
EXTENSIONS
More terms from Harvey P. Dale, Nov 02 2011
STATUS
approved