# [seqfan] Re: n X n binary array quasi-packing problem

Rob Pratt Rob.Pratt at sas.com
Thu Feb 9 21:21:49 CET 2017

```The conjecture is true at least up through n = 50.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Ron Hardin
Sent: Thursday, February 09, 2017 11:19 AM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: n X n binary array quasi-packing problem

Probably true but the counterspeculation would be that there's some larger-period arrangement that fits better for big n, if it's below the upper bound.
I'll email when I put the sequence up.
rhhardin at mindspring.com rhhardin at att.net (either)

From: Richard J. Mathar <mathar at mpia-hd.mpg.de>
To: seqfan at seqfan.eu
Sent: Thursday, February 9, 2017 7:27 AM
Subject: [seqfan] Re: n X n binary array quasi-packing problem

On behalf of http://list.seqfan.eu/pipermail/seqfan/2017-February/017253.html :

This leads to the immediate conjecture that the case with b=8 is given by

G.f.: -x^2*(2+5*x+3*x^2+3*x^3+x^4)/(1+x+x^2)^2/(x-1)^3 .
<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
a(n) = +a(n-1) +2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7).

27*a(n) = -4-9*n+21*n^2 +4*c(n) -12*c(n-2)-c(n-3).
where c(n) = (-1)^n*A099254(n)
and A033582 is a trisection.

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