minimal perimeter of a polyhex

[David W. Wilson]

As far as I can determine:

a(0) =
    0, if n = 0
    a(n-1) + 2(#{k >= 0: n = [(k^2+15)/12]})

I initially hoped for a solution of the form

    a(n) = 2[sqrt(12n + something)]

but a(n) looks a little to bumpy.

> -----Original Message-----
> From: Tanya Khovanova [mailto:mathoflove-seqfan at yahoo.com]
> Sent: Tuesday, March 04, 2008 9:21 AM
> To: SeqFan
> Subject: minimal perimeter of a polyhex
> 
> Dear SeqFans,
> 
> I just submitted the sequence:
> 
> 6, 10, 12, 14, 16, 18, 18, 20, 22, 22, 24, 24,
> Minimal perimeter of a polyhex with n cells.
> 
> I am surprised that this sequence wasn't there.
> 
> I calculated it manually. Anyone has a program dealing with polyhexes?
> Can someone extend it? Is there are program for polyhexes somewhere
> available for free use?
> 
> Best, Tanya