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A204711 Number of (n+1)X7 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero 1
193, 1361, 8705, 58449, 382849, 2542369, 16748161, 110871041, 731709057, 4838473473, 31954317953, 211206670209, 1395251843713, 9220409667201, 60918293373569, 402541765541505, 2659689937121921, 17574356285235841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 6 of A204713

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of formula

FORMULA

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).

Empirical formula confirmed by Robert Israel, Jun 11 2018: see link.

EXAMPLE

Some solutions for n=4

..1..0..1..0..1..0..1....0..1..0..1..0..1..1....1..0..1..0..1..1..0

..0..1..0..1..0..1..0....1..0..1..0..1..1..0....0..1..1..1..0..1..1

..1..0..1..1..1..1..1....1..1..1..1..0..1..1....1..1..0..1..1..1..0

..0..1..0..1..0..1..0....0..1..0..1..1..0..1....0..1..1..0..1..0..1

..1..0..1..0..1..1..1....1..0..1..1..0..1..0....1..1..0..1..1..1..1

MAPLE

Configs:=  [seq(convert(2^7+i, base, 2)[1..7], i=0..2^7-1)]:

Compatible:= proc(i, j)

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

end proc:

T:= Matrix(128, 128, Compatible):

u:= Vector[row](128, 1):

v:= Vector(128, 1):

TV[0]:= v:

for n from 1 to 40 do TV[n]:= T . TV[n-1] od:

seq(1+u . TV[n], n=1..40); # Robert Israel, Jun 11 2018

CROSSREFS

Sequence in context: A340230 A142564 A174521 * A125647 A166540 A178265

Adjacent sequences:  A204708 A204709 A204710 * A204712 A204713 A204714

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 18 2012

STATUS

approved

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)