A221022 - OEIS

%I #8 Aug 03 2018 08:12:42

%S 8,168,3474,62944,1038208,16735744,268269568,4294303744,68716822528,

%T 1099501010944,17592143577088,281474806841344,4503598947893248,

%U 72057591320018944,1152921493735211008,18446744030223007744

%N Equals one maps: number of n X 4 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal, vertical and antidiagonal neighbors in a random 0..3 n X 4 array.

%C Column 4 of A221024.

%H R. H. Hardin, <a href="/A221022/b221022.txt">Table of n, a(n) for n = 1..55</a>

%F Empirical: a(n) = 20*a(n-1) -64*a(n-2) for n>5.

%F Conjectures from _Colin Barker_, Aug 03 2018: (Start)

%F G.f.: 2*x*(4 + 4*x + 313*x^2 + 2108*x^3 + 832*x^4) / ((1 - 4*x)*(1 - 16*x)).

%F a(n) = 16^n - 81*2^(2*n-3) for n>3.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A221024.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2012