

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
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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(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) 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



