A205257 - OEIS

A205257

Number of (n+2) X 3 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..1 introduced in row major order.

240, 1814, 13728, 103876, 785920, 5946280, 44989988, 340397184, 2575465940, 19486134776, 147433307220, 1115489560600, 8439863289268, 63856529812904, 483142470500100, 3655485938158424, 27657633637846868, 209259373825754344

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OFFSET

1,1

COMMENTS

Column 1 of A205264.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 6*a(n-1) +7*a(n-2) +32*a(n-3) +34*a(n-4) +14*a(n-5) -20*a(n-6) -16*a(n-7).

Empirical g.f.: 2*x*(120 + 187*x + 582*x^2 + 565*x^3 + 180*x^4 - 352*x^5 - 256*x^6) / (1 - 6*x - 7*x^2 - 32*x^3 - 34*x^4 - 14*x^5 + 20*x^6 + 16*x^7). - Colin Barker, Jun 11 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

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

CROSSREFS

Cf. A205264.

Sequence in context: A290655 A212781 A205264 * A049335 A004009 A269033

Adjacent sequences: A205254 A205255 A205256 * A205258 A205259 A205260

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 24 2012

STATUS

approved