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A204711 Number of (n+1)X7 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero.

%I A204711 #12 Jul 22 2025 18:15:08
%S A204711 193,1361,8705,58449,382849,2542369,16748161,110871041,731709057,
%T A204711 4838473473,31954317953,211206670209,1395251843713,9220409667201,
%U A204711 60918293373569,402541765541505,2659689937121921,17574356285235841
%N A204711 Number of (n+1)X7 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero.
%C A204711 Column 6 of A204713
%H A204711 R. H. Hardin, <a href="/A204711/b204711.txt">Table of n, a(n) for n = 1..210</a>
%H A204711 Robert Israel, <a href="/A204711/a204711.pdf">Maple-assisted proof of formula</a>
%F A204711 Empirical: a(n) = 4*a(n-1) +45*a(n-2) -126*a(n-3) -642*a(n-4) +1332*a(n-5) +3620*a(n-6) -5624*a(n-7) -6800*a(n-8) +8192*a(n-9).
%F A204711 Empirical formula confirmed by _Robert Israel_, Jun 11 2018: see link.
%e A204711 Some solutions for n=4
%e A204711 ..1..0..1..0..1..0..1....0..1..0..1..0..1..1....1..0..1..0..1..1..0
%e A204711 ..0..1..0..1..0..1..0....1..0..1..0..1..1..0....0..1..1..1..0..1..1
%e A204711 ..1..0..1..1..1..1..1....1..1..1..1..0..1..1....1..1..0..1..1..1..0
%e A204711 ..0..1..0..1..0..1..0....0..1..0..1..1..0..1....0..1..1..0..1..0..1
%e A204711 ..1..0..1..0..1..1..1....1..0..1..1..0..1..0....1..1..0..1..1..1..1
%p A204711 Configs:=  [seq(convert(2^7+i,base,2)[1..7],i=0..2^7-1)]:
%p A204711 Compatible:= proc(i,j)
%p A204711 if andmap(k -> Configs[i][k]*Configs[j][k+1]+Configs[i][k+1]*Configs[j][k] = 1, [$1..6]) then 1 else 0 fi
%p A204711 end proc:
%p A204711 T:= Matrix(128,128,Compatible):
%p A204711 u:= Vector[row](128, 1):
%p A204711 v:= Vector(128, 1):
%p A204711 TV[0]:= v:
%p A204711 for n from 1 to 40 do TV[n]:= T . TV[n-1] od:
%p A204711 seq(1+u . TV[n],n=1..40); # _Robert Israel_, Jun 11 2018
%K A204711 nonn
%O A204711 1,1
%A A204711 _R. H. Hardin_, Jan 18 2012