A202050 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.

1392, 5216, 15760, 41088, 95984, 205792, 411696, 777760, 1400080, 2418432, 4030832, 6511456, 10232400, 15689792, 23534800, 34610112, 49992496, 71042080, 99459024, 137348288, 187293232, 252438816, 336585200, 444292576, 580998096

Offset

1,1

Comments

Column 6 of A202052.

Links

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

Formula

Empirical: a(n) = (1/1260)*n^8 + (11/315)*n^7 + (59/90)*n^6 + (308/45)*n^5 + (7807/180)*n^4 + (7667/45)*n^3 + (14139/35)*n^2 + (17876/35)*n + 256.

Conjectures from Colin Barker, May 26 2018: (Start)

G.f.: 16*x*(87 - 457*x + 1183*x^2 - 1869*x^3 + 1925*x^4 - 1307*x^5 + 567*x^6 - 143*x^7 + 16*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for n=3:
  0 0 0 0 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 1 1 1 1 1
  0 1 0 1 0 0 0 0     1 0 1 0 1 0 0 0     0 1 0 0 0 0 0 0
  0 1 0 0 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 1 1 1 1 1
  0 1 0 1 0 0 0 0     0 1 0 1 0 0 0 0     0 1 0 0 0 0 0 0
  0 1 0 1 0 0 0 0     0 1 0 1 0 1 0 1     1 0 1 0 1 0 0 0

Crossrefs

Cf. A202052.

Sequence in context: A031983 A249970 A069422 * A236520 A235657 A094666

Adjacent sequences: A202047 A202048 A202049 * A202051 A202052 A202053

Keyword

nonn

Author

R. H. Hardin, Dec 10 2011

Status

approved