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A227259 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 two or less, with rows and columns of the latter in lexicographically nondecreasing order. 1
3, 9, 23, 50, 96, 168, 274, 423, 625, 891, 1233, 1664, 2198, 2850, 3636, 4573, 5679, 6973, 8475, 10206, 12188, 14444, 16998, 19875, 23101, 26703, 30709, 35148, 40050, 45446, 51368, 57849, 64923, 72625, 80991, 90058, 99864, 110448, 121850, 134111 (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 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1.

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

G.f.: x*(3 - 6*x + 8*x^2 - 5*x^3 + 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..0....1..1....1..1....1..1....1..1....1..0....1..1....1..1....0..0....1..1

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

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

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

CROSSREFS

Column 2 of A227263.

Sequence in context: A147271 A230119 A146693 * A064551 A005783 A263330

Adjacent sequences:  A227256 A227257 A227258 * A227260 A227261 A227262

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 04 2013

STATUS

approved

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Last modified August 3 21:09 EDT 2021. Contains 346441 sequences. (Running on oeis4.)