A183980 1/4 the number of (n+1) X 4 binary arrays with all 2 X 2 subblock sums the same.

9, 11, 14, 20, 30, 50, 86, 158, 294, 566, 1094, 2150, 4230, 8390, 16646, 33158, 66054, 131846, 263174, 525830, 1050630, 2100230, 4198406, 8394758, 16785414, 33566726, 67125254, 134242310, 268468230, 536920070, 1073807366, 2147581958, 4295098374

Offset

1,1

Comments

Column 3 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 07 2018: (Start)

G.f.: x*(9 - 16*x - 19*x^2 + 32*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = (3*2^(n/2) + 2^n + 12) / 2 for n even.

a(n) = 2^((n-5)/2+3) + 2^(n-1) + 6 for n odd.

(End)

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

Example

Some solutions for 5 X 4.
..0..1..0..1....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
..1..0..1..0....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
..0..1..0..1....1..1..1..1....0..0..1..1....0..1..0..1....1..1..1..0

Crossrefs

Cf. A183986.

Sequence in context: A279519 A307188 A212816 * A101754 A348614 A113339

Adjacent sequences: A183977 A183978 A183979 * A183981 A183982 A183983

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved