Is sequence A084894 plausible?
Brendan McKay
bdm at cs.anu.edu.au
Mon Sep 6 09:39:22 CEST 2004
ID Number: A084894
Sequence: 0,0,2,20,112,696,5008,40280,362760,3628504,39916152,
479000272,6227017600,8717828,1288,1307674342408,
20922789832080,355687427952808,6402373705217304,
1216451004073,80704,2432902008173142656
Name: Number of permutations of length n such that at least one absolute
difference between consecutive elements has a distinct partner.
Comments: a(n)=n!-A006967(n)
I suggest that this sequence is broken as the small values interspersed
with the large values are impossible. Sequence A006967 (graceful
permutations) is ok. Graceful permutations are a vanishing fraction
of all permutations so A084894(n) should be close to n!.
Brendan.
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