A204712 Number of (n+1) X 8 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

385, 3473, 28161, 239425, 1992321, 16748161, 140090241, 1174759297, 9838208513, 82449830017, 690711971457, 5787565930753, 48489078457729, 406275347589249, 3403932556101121, 28520064001053825, 238954333647573121

Offset: 1

Author

R. H. Hardin, Jan 18 2012

Keywords

• nonn

Comments

Column 7 of A204713.

Examples

			Some solutions for n=4
..0..1..1..1..1..1..1..1....1..1..0..1..0..1..0..1....0..1..0..1..1..0..1..0
..1..0..1..0..1..0..1..0....0..1..1..1..1..0..1..1....1..0..1..0..1..1..1..1
..1..1..0..1..0..1..1..1....1..1..0..1..0..1..1..0....0..1..0..1..0..1..0..1
..0..1..1..0..1..0..1..0....0..1..1..0..1..0..1..1....1..1..1..1..1..1..1..0
..1..1..0..1..0..1..0..1....1..1..0..1..0..1..0..1....0..1..0..1..0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of formula

Crossrefs

Cf. A204713.

Programs

Maple

Configs:=  [seq(convert(2^8+i,base,2)[1..8],i=0..2^8-1)]:
Compatible:= proc(i,j)
if andmap(k -> Configs[i][k]*Configs[j][k+1]+Configs[i][k+1]*Configs[j][k] = 1, [$1..7]) then 1 else 0 fi
end proc:
T:= Matrix(256,256,Compatible):
u:= Vector[row](256, 1):
v:= Vector(256, 1):
TV[0]:= v:
for n from 1 to 30 do TV[n]:= T . TV[n-1] od:
seq(1+ u . TV[n],n=1..30); # Robert Israel, Jun 19 2018

Formula

Empirical: a(n) = 8*a(n-1) +50*a(n-2) -389*a(n-3) -790*a(n-4) +6534*a(n-5) +3836*a(n-6) -45232*a(n-7) +9360*a(n-8) +108928*a(n-9) -82304*a(n-10).

Empirical formula confirmed by Robert Israel, Jun 19 2018: see link.