A200462 - OEIS

%I #16 Dec 12 2023 08:40:21

%S 2,3,5,8,13,20,29,43,63,91,130,184,262,370,519,724,1010,1408,1955,

%T 2705,3735,5157,7107,9775,13418,18406,25227,34529,47200,64455,87969,

%U 119952,163415,222427,302568,411334,558808,758640,1029312,1395882,1891970

%N Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 2.

%H R. H. Hardin, <a href="/A200462/b200462.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) - a(n + 1) + a(n + 3) + a(n + 4) - 5*a(n + 5) + 2*a(n + 6) + 2*a(n + 7) - 2*a(n + 8) - 2*a(n + 9) + 5*a(n + 10) - a(n + 11) - 2*a(n + 12) + 2*a(n + 13) - 2*a(n + 15) + a(n + 16) = 0. - _Robert Israel_, Dec 11 2023

%e Some solutions for n=6:

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

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

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

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

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

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

%p Configs:=  [seq(convert(16+i,base,2)[1..4],i=0..15)]:

%p Compatible:= proc(i,j)

%p  if not Configs[i][2..4]=Configs[j][1..3] then return 0 fi;

%p  if convert(Configs[i],`+`) mod 2 <= Configs[j][4]

%p  then 1 else 0

%p  fi

%p end proc:

%p T:= Matrix(16,16,Compatible):

%p initconfigs:= select(t -> t[1] <= t[2] and t[1]+t[2] mod 2 <= t[3] and t[1]+t[2]+t[3] mod 2 <= t[4], Configs):

%p u0:= Vector(16, i -> `if`(member(Configs[i],initconfigs),1,0)):

%p 2,3,5,8,seq(u0^%T . T^i . e, i=1..40); # _Robert Israel_, Dec 11 2023

%Y Column 1 of A200469.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 18 2011