A224739 - OEIS

%I #12 Jun 19 2019 00:16:18

%S 38,152,565,2326,9554,40297,170754,728996,3120401,13387658,57499978,

%T 247151833,1062764258,4571134864,19664166357,84599301422,363983008394,

%U 1566063674345,6738231845242,28992616966540,124747487937041

%N Number of (n+1) X 3 0..1 matrices with each 2 X 2 permanent equal.

%H R. H. Hardin, <a href="/A224739/b224739.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A224739/a224739.pdf">Maple-assisted proof of empirical recurrence</a>

%F Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 34*a(n-3) + 59*a(n-4) + 27*a(n-5) - 87*a(n-6) + 36*a(n-7).

%F Empirical g.f.: x*(38 - 114*x - 233*x^2 + 727*x^3 + 153*x^4 - 1083*x^5 + 504*x^6) / ((1 - x)*(1 - 5*x + 3*x^2)*(1 - 3*x^2)*(1 - x - 4*x^2)). - _Colin Barker_, Sep 05 2018

%F Empirical recurrence confirmed (see link). - _Robert Israel_, Jun 18 2019

%e Some solutions for n=3:

%e ..0..0..1....1..0..0....1..0..1....0..0..1....1..0..0....1..0..1....1..0..1

%e ..0..0..0....0..0..1....0..1..0....1..0..0....1..0..0....1..1..1....1..0..1

%e ..1..1..1....1..0..0....1..0..1....1..0..1....0..0..1....0..1..0....0..0..0

%e ..0..0..0....1..0..0....1..1..1....1..0..1....1..0..1....1..1..1....1..1..1

%Y Column 2 of A224745.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 17 2013