A200462 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.

2, 3, 5, 8, 13, 20, 29, 43, 63, 91, 130, 184, 262, 370, 519, 724, 1010, 1408, 1955, 2705, 3735, 5157, 7107, 9775, 13418, 18406, 25227, 34529, 47200, 64455, 87969, 119952, 163415, 222427, 302568, 411334, 558808, 758640, 1029312, 1395882, 1891970

Offset: 1

Author

R. H. Hardin, Nov 18 2011

Keywords

• nonn

Examples

			Some solutions for n=6:
  0   1   0   0   0   0   1   1   0   0   0   0   0   1   1   1
  0   1   1   0   0   0   1   1   1   0   1   0   1   1   1   1
  1   1   1   0   0   0   0   1   1   0   1   1   1   1   0   0
  1   1   0   1   0   0   0   1   0   1   1   1   0   1   0   0
  0   1   0   1   1   0   1   1   1   1   1   0   0   0   0   1
  0   1   0   0   1   0   1   0   1   1   0   1   1   1   1   0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 1 of A200469.

Programs

Maple

Configs:=  [seq(convert(16+i,base,2)[1..4],i=0..15)]:
Compatible:= proc(i,j)
 if not Configs[i][2..4]=Configs[j][1..3] then return 0 fi;
 if convert(Configs[i],`+`) mod 2 <= Configs[j][4]
 then 1 else 0
 fi
end proc:
T:= Matrix(16,16,Compatible):
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):
u0:= Vector(16, i -> `if`(member(Configs[i],initconfigs),1,0)):
2,3,5,8,seq(u0^%T . T^i . e, i=1..40); # Robert Israel, Dec 11 2023

Formula

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