A281464 - OEIS

%I #8 Feb 20 2019 05:30:08

%S 4,17,24,60,133,283,634,1419,3092,6849,15213,33509,74017,163898,

%T 361980,799660,1768383,3908128,8635736,19089245,42191413,93242838,

%U 206088583,455499706,1006707139,2224999897,4917670483,10868814633,24021891696

%N Number of n X 3 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281464/b281464.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 3*a(n-3) - 3*a(n-4) - 4*a(n-5) + 4*a(n-6) - 4*a(n-7) for n>9.

%F Empirical g.f.: x*(4 + 9*x - 10*x^2 - 26*x^4 + 12*x^5 + 12*x^6 - 24*x^7 + 16*x^8) / (1 - 2*x - 3*x^3 + 3*x^4 + 4*x^5 - 4*x^6 + 4*x^7). - _Colin Barker_, Feb 19 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A281469.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 22 2017