A227121 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order.

3, 7, 13, 23, 40, 68, 112, 178, 273, 405, 583, 817, 1118, 1498, 1970, 2548, 3247, 4083, 5073, 6235, 7588, 9152, 10948, 12998, 15325, 17953, 20907, 24213, 27898, 31990, 36518, 41512, 47003, 53023, 59605, 66783, 74592, 83068, 92248, 102170, 112873

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (11/24)*n^2 + (31/12)*n.

Conjectures from Colin Barker, Sep 07 2018: (Start)

G.f.: x*(3 - 8*x + 8*x^2 - 2*x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=4:
..1..0....0..0....1..0....1..1....1..1....1..0....0..0....1..1....0..0....1..1
..1..0....0..0....1..0....1..0....1..1....0..0....0..0....1..1....0..1....0..0
..0..0....0..0....1..0....1..0....1..1....0..0....0..1....1..0....0..1....0..0
..0..0....0..0....1..0....1..0....1..1....0..0....0..1....1..0....0..0....0..1

Crossrefs

Column 2 of A227125.

Sequence in context: A122886 A154691 A306902 * A078447 A066624 A317783

Adjacent sequences: A227118 A227119 A227120 * A227122 A227123 A227124

Keyword

nonn

Author

R. H. Hardin, Jul 01 2013

Status

approved