The OEIS is supported by the many generous donors to the OEIS Foundation.

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

2

`%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
`