A207399 - OEIS

%I #8 Mar 05 2018 05:36:08

%S 9,81,289,729,1521,2809,4761,7569,11449,16641,23409,32041,42849,56169,

%T 72361,91809,114921,142129,173889,210681,253009,301401,356409,418609,

%U 488601,567009,654481,751689,859329,978121,1108809,1252161,1408969

%N Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 4 of A207403.

%H R. H. Hardin, <a href="/A207399/b207399.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1.

%F Conjectures from _Colin Barker_, Mar 05 2018: (Start)

%F G.f.: x*(9 + 36*x - 26*x^2 + 4*x^3 + x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A207403.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2012