|
%I #8 Feb 22 2019 10:04:50
%S 4,29,104,467,2197,9645,43335,195508,876170,3935424,17683045,79404264,
%T 356636392,1601851743,7194361447,32312564136,145128246079,
%U 651823344848,2927580000227,13148849554269,59056335597781,265243849656279
%N Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A295842/b295842.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + a(n-2) + 12*a(n-3) - 30*a(n-4) + 3*a(n-5) - 6*a(n-6) + 6*a(n-7) + 5*a(n-8) + 2*a(n-9).
%F Empirical g.f.: x*(4 + 13*x - 16*x^2 - 26*x^3 - 3*x^4 + 11*x^6 + 7*x^7 + 2*x^8) / (1 - 4*x - x^2 - 12*x^3 + 30*x^4 - 3*x^5 + 6*x^6 - 6*x^7 - 5*x^8 - 2*x^9). - _Colin Barker_, Feb 22 2019
%e Some solutions for n=7:
%e ..0..0..0. .0..1..1. .0..0..1. .1..1..0. .0..1..0. .0..1..0. .1..0..1
%e ..0..0..1. .0..0..0. .1..0..1. .0..0..1. .1..0..0. .0..1..0. .0..1..0
%e ..1..1..0. .0..1..1. .1..0..1. .0..1..0. .1..0..0. .0..0..0. .0..0..0
%e ..0..0..0. .1..0..0. .0..1..0. .0..0..0. .0..1..0. .1..1..0. .0..0..0
%e ..1..1..0. .1..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..1. .0..0..0
%e ..0..0..0. .0..0..1. .0..1..0. .0..1..0. .0..1..1. .0..1..0. .1..0..0
%e ..1..1..1. .0..0..1. .0..1..1. .0..1..0. .0..1..0. .0..0..1. .0..1..1
%Y Column 3 of A295847.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 29 2017
| 