A270111 - OEIS

%I #7 Mar 22 2018 06:51:11

%S 0,8,112,1176,10976,96040,806736,6588344,52706752,415065672,

%T 3228288560,24857821912,189823367328,1439493868904,10851569165584,

%U 81386768741880,607687873272704,4519678557465736,33498794014157808,247518866882388248

%N Number of n X 1 0..7 arrays with some element plus some horizontally or vertically adjacent neighbor totalling seven exactly once.

%C Column 1 of A270118.

%H R. H. Hardin, <a href="/A270111/b270111.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 14*a(n-1) - 49*a(n-2).

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

%F G.f.: 8*x^2 / (1 - 7*x)^2.

%F a(n) = 8*7^(n-2)*(n-1).

%F (End)

%e Some solutions for n=4:

%e ..5. .5. .6. .5. .0. .4. .7. .4. .4. .5. .7. .0. .7. .7. .1. .5

%e ..6. .5. .2. .2. .7. .3. .1. .3. .5. .2. .1. .4. .6. .2. .3. .0

%e ..7. .2. .2. .2. .1. .3. .6. .1. .3. .4. .6. .3. .1. .6. .4. .7

%e ..0. .3. .5. .3. .2. .6. .6. .5. .4. .0. .7. .6. .7. .1. .5. .7

%Y Cf. A270118.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 11 2016