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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 20:37 EDT 2019. Contains 324380 sequences. (Running on oeis4.)