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

1,1

Links

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

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

Example

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

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

Crossrefs

Column 1 of A200469.

Sequence in context: A326594 A045842 A324741 * A088795 A156145 A216053

Adjacent sequences: A200459 A200460 A200461 * A200463 A200464 A200465

Keyword

nonn

Author

R. H. Hardin, Nov 18 2011

Status

approved