A183985 1/4 the number of (n+1) X 9 binary arrays with all 2 X 2 subblock sums the same.

153, 155, 158, 164, 174, 194, 230, 302, 438, 710, 1238, 2294, 4374, 8534, 16790, 33302, 66198, 131990, 263318, 525974, 1050774, 2100374, 4198550, 8394902, 16785558, 33566870, 67125398, 134242454, 268468374, 536920214, 1073807510, 2147582102

Offset

1,1

Comments

Column 8 of A183986.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 09 2018: (Start)

G.f.: x*(153 - 304*x - 307*x^2 + 608*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 3*2^(n/2-1) + 2^(n-1) + 150 for n even.

a(n) = 2^(n-1) + 2^((n+1)/2) + 150 for n odd.

(End)

Example

Some solutions for 5 X 9:
..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1
..1..1..0..0..0..1..1..0..0....1..0..1..1..0..0..0..0..0
..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1
..1..1..0..0..0..1..1..0..0....1..0..1..1..0..0..0..0..0
..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1

Crossrefs

Cf. A183986.

Sequence in context: A095226 A346630 A165340 * A184045 A203603 A272767

Adjacent sequences: A183982 A183983 A183984 * A183986 A183987 A183988

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved