[seqfan] Re: Permutations with even sums of adjacent triples

hv at crypt.org hv at crypt.org
Sun Dec 17 22:44:17 CET 2017

"Richard J. Mathar" <mathar at mpia-hd.mpg.de> wrote:
:Les Reid asks in http://people.missouristate.edu/lesreid/POW12_1011.html:
:how many permutations of [n] exist such that the sum of 3 adjacent
:numbers is always even? This seems to start
:6,4,24,0,144,0,0,0 (n>=3)

I think it will be 0 for all n > 7.

In any permutation P = [ p_1 .. p_n ] we need p_i == p_{i+3} (mod 2)
for 1 <= i <= n - 3. We also need each triple to have one even and
two odd elements.

The last opportunity for such a pattern is 1 .. 7 => EOOEOOE; after
that we need too many odd numbers.


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