A296322 - OEIS

%I #8 Feb 23 2019 04:21:36

%S 1,5,11,23,54,122,278,634,1438,3274,7451,16943,38547,87691,199477,

%T 453789,1032300,2348324,5342108,12152500,27645148,62888676,143062485,

%U 325446157,740342261,1684169937,3831239423,8715507347,19826499874,45102377086

%N Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

%H R. H. Hardin, <a href="/A296322/b296322.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) - 2*a(n-4) + 4*a(n-5) - 3*a(n-6) + 2*a(n-7) - a(n-8).

%F Empirical g.f.: x*(1 + 3*x + 2*x^2 + 2*x^3 + x^4 - x^5 + x^6 - x^7) / ((1 + x^2)*(1 - 2*x - 2*x^3 + 2*x^4 - 2*x^5 + x^6)). - _Colin Barker_, Feb 23 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 3 of A296327.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 10 2017