A227265 - OEIS

A227265

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 three or less, with rows and columns of the latter in lexicographically nondecreasing order.

3, 8, 16, 30, 54, 93, 153, 241, 365, 534, 758, 1048, 1416, 1875, 2439, 3123, 3943, 4916, 6060, 7394, 8938, 10713, 12741, 15045, 17649, 20578, 23858, 27516, 31580, 36079, 41043, 46503, 52491, 59040, 66184, 73958, 82398, 91541, 101425, 112089, 123573

(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 - (1/24)*n^2 + (47/12)*n - 1.

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

G.f.: x*(3 - 7*x + 6*x^2 - x^4) / (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..1....1..1....1..1....1..1....1..0....1..1....1..0....1..1....1..0....1..0

..1..1....1..0....1..0....1..1....0..0....1..1....1..0....1..1....1..0....1..1

..1..0....1..1....1..1....1..1....0..0....1..1....1..1....1..0....0..0....1..1

..1..0....0..1....1..1....1..1....0..0....0..1....1..1....0..0....0..0....0..0

CROSSREFS

Column 2 of A227269.

Sequence in context: A000233 A002624 A293358 * A295960 A068039 A188123

Adjacent sequences: A227262 A227263 A227264 * A227266 A227267 A227268

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 04 2013

STATUS

approved

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