A204712 Number of (n+1)X8 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero

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

Offset

1,1

Comments

Column 7 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) = 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.

Example

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

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

Crossrefs

Sequence in context: A200525 A225711 A351696 * A237102 A264421 A063390

Adjacent sequences: A204709 A204710 A204711 * A204713 A204714 A204715

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved