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

193, 1361, 8705, 58449, 382849, 2542369, 16748161, 110871041, 731709057, 4838473473, 31954317953, 211206670209, 1395251843713, 9220409667201, 60918293373569, 402541765541505, 2659689937121921, 17574356285235841

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