A279979 - OEIS

A279979

Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I #9 Sep 20 2023 19:19:37

%S 0,9,50,221,822,2669,8068,23169,64250,173509,459148,1195219,3069280,

%T 7791834,19587853,48827241,120818815,297018329,725970958,1765237102,

%U 4272245780,10296018246,24717636634,59130589267,140997069400,335205034089,794714054209,1879307452216

%N Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%C Row 3 of A279977.

%H R. H. Hardin, <a href="/A279979/b279979.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) -33*a(n-2) +60*a(n-3) -36*a(n-4) -78*a(n-5) +199*a(n-6) -165*a(n-7) -33*a(n-8) +200*a(n-9) -180*a(n-10) +66*a(n-11) +22*a(n-12) -78*a(n-13) +84*a(n-14) -40*a(n-15) -21*a(n-16) +15*a(n-17) -3*a(n-18) +18*a(n-19) +6*a(n-20) -4*a(n-21) -3*a(n-22) -3*a(n-23) -a(n-24) for n>30.

%e Some solutions for n=4:

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

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

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

%Y Cf. A279977.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 24 2016