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A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 1
0, 4, 14, 40, 110, 280, 698, 1696, 4052, 9564, 22330, 51728, 118998, 272228, 619804, 1405456, 3175966, 7155320, 16078698, 36048008, 80656900, 180149700, 401740002, 894646944, 1989842814, 4420825196, 9811946668, 21757950712, 48209235558 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) - a(n-4) + 30*a(n-5) + 4*a(n-6) - 24*a(n-7) - 4*a(n-8) + 8*a(n-9).
Empirical g.f.: 2*x^2*(1 - x)*(1 + x)*(2 - x - 8*x^2 - x^3 + 6*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)^2). - Colin Barker, Feb 20 2019
EXAMPLE
Some solutions for n=4:
..0..1..1..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..0..0
CROSSREFS
Row 2 of A281765.
Sequence in context: A023003 A001872 A054443 * A072674 A202900 A238117
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 29 2017
STATUS
approved

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Last modified July 16 16:12 EDT 2024. Contains 374356 sequences. (Running on oeis4.)