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

Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4).

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)

The above empirical formula is correct. See note from Andrew Howroyd in A183986.

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