[seqfan] Re: b-files for apparently matching sequences?

Maximilian Hasler maximilian.hasler at gmail.com
Tue Jun 29 17:52:41 CEST 2010

> What to do with the b-files?
> %N A020701 Pisot sequences E(3,5), P(3,5).
> %N xxxxxxx Number of permutations of 1..n with i-1<=p(i)<=i+1
> %C xxxxxxx (Empirical) a(n)=A020701(n-3)
> %H A020701 R. H. Hardin, <a href="b020701">Table of n,a(n) for n=0..97</a>

I get :
{for(n=1,99, v=vector(n,i,i); print1( sum(k=1,n!,
vecmax(abs(numtoperm(n,k)-v))<=1),", "))}

1, 2, 3, 5, 8, 13, 21, 34, 55,

which are the Fibonacci numbers.

Indeed, there is:

%C A000045 F(n) = number of permutations p of 1,2,3,...,n such that |k-p(k)|<=1
               for k=1,2,...,n. (For <=2 and <=3, see A002524 and
A002526.). - Clark
               Kimberling (ck6(AT)evansville.edu), Nov 28 2004

and there already is

%F A020701 a(n) = Fib(n+4).


%F A020695 a(n) = Fib(n+3);

So there is nothing new about these two, at least.


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