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Number of n X 1 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.
2

%I #7 Mar 22 2018 06:51:18

%S 0,7,84,756,6048,45360,326592,2286144,15676416,105815808,705438720,

%T 4655895552,30474952704,198087192576,1279948013568,8228237230080,

%U 52660718272512,335712078987264,2132759090036736,13507474236899328

%N Number of n X 1 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.

%C Column 1 of A269902.

%H R. H. Hardin, <a href="/A269895/b269895.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 36*a(n-2).

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

%F G.f.: 7*x^2 / (1 - 6*x)^2.

%F a(n) = 7*6^(n-2)*(n-1).

%F (End)

%e Some solutions for n=4:

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

%e ..2. .1. .4. .3. .6. .3. .2. .4. .2. .5. .1. .6. .1. .5. .2. .4

%e ..5. .5. .2. .1. .0. .0. .6. .2. .0. .4. .5. .2. .6. .1. .1. .2

%e ..6. .5. .2. .1. .0. .4. .6. .5. .1. .4. .0. .4. .0. .2. .4. .6

%Y Cf. A269902.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 07 2016