A295980 - OEIS

%I #7 Feb 22 2019 11:22:45

%S 1,15,44,110,581,2354,8452,35474,146560,580023,2356053,9619854,

%T 38867687,157518881,639985423,2594957421,10522265148,42696678744,

%U 173200350255,702516695938,2849908304750,11560960945608,46896382885056

%N Number of n X 3 0..1 arrays with each 1 adjacent to 2 or 3 king-move neighboring 1s.

%H R. H. Hardin, <a href="/A295980/b295980.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 21*a(n-3) - 44*a(n-4) - 12*a(n-5) - 34*a(n-6) + 33*a(n-7) + 4*a(n-8) + 14*a(n-9) + a(n-10).

%F Empirical g.f.: x*(1 + 11*x - 14*x^2 - 57*x^3 - 42*x^4 - 2*x^5 + 38*x^6 + 18*x^7 + 15*x^8 + x^9) / (1 - 4*x + 2*x^2 - 21*x^3 + 44*x^4 + 12*x^5 + 34*x^6 - 33*x^7 - 4*x^8 - 14*x^9 - x^10). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A295985.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 01 2017