A269822 - OEIS

%I #7 Mar 22 2018 06:52:07

%S 0,5,40,240,1280,6400,30720,143360,655360,2949120,13107200,57671680,

%T 251658240,1090519040,4697620480,20132659200,85899345920,365072220160,

%U 1546188226560,6528350289920,27487790694400,115448720916480

%N Number of n X 1 0..4 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling four exactly once.

%C Column 1 of A269829.

%H R. H. Hardin, <a href="/A269822/b269822.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 16*a(n-2).

%F Conjectures from _Colin Barker_, Mar 22 2018: (Start)

%F G.f.: 5*x^2 / (1 - 4*x)^2.

%F a(n) = 5*4^(n-2)*(n-1).

%F (End)

%e Some solutions for n=4:

%e ..1. .2. .2. .4. .4. .3. .2. .4. .4. .0. .0. .0. .2. .3. .3. .2

%e ..1. .3. .3. .2. .3. .4. .2. .4. .0. .1. .0. .3. .3. .0. .1. .4

%e ..1. .1. .2. .4. .1. .1. .3. .3. .0. .4. .4. .4. .4. .1. .0. .0

%e ..3. .0. .2. .0. .0. .3. .3. .1. .3. .0. .1. .0. .0. .3. .3. .3

%Y Cf. A269829.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 05 2016