A252725 - OEIS

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A252725

Number of (6+2) X (n+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

165, 154, 170, 178, 214, 262, 270, 354, 434, 466, 622, 790, 846, 1170, 1490, 1618, 2254, 2902, 3150, 4434, 5714, 6226, 8782, 11350, 12366, 17490, 22610, 24658, 34894, 45142, 49230, 69714, 90194, 98386, 139342, 180310, 196686, 278610, 360530, 393298

(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) = -a(n-1) +3*a(n-3) +3*a(n-4) -2*a(n-6) -2*a(n-7) for n>9.

Empirical g.f.: x*(165 + 319*x + 324*x^2 - 147*x^3 - 565*x^4 - 496*x^5 - 182*x^6 + 86*x^7 + 8*x^8) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 - 2*x^3)). - Colin Barker, Dec 06 2018

EXAMPLE

Some solutions for n=4:

..0..1..1..0..1..1....0..1..0..0..1..0....0..1..0..0..1..0....0..1..0..0..2..0

..2..1..2..2..1..2....0..0..1..0..0..1....1..1..2..1..1..2....0..0..1..0..0..2

..1..1..0..1..1..0....0..2..2..0..2..2....2..1..1..2..1..1....0..3..3..0..3..3

..0..1..1..0..1..1....0..3..0..0..1..0....0..1..0..0..1..0....0..2..0..0..1..0

..2..1..2..2..1..2....0..0..3..0..0..1....1..1..2..1..1..2....0..0..2..0..0..1

..1..1..0..1..1..0....0..2..2..0..2..2....3..1..1..2..1..1....0..3..3..0..3..3

..3..1..1..0..1..1....0..3..0..0..3..0....0..1..0..0..1..0....0..1..0..0..2..0

..2..1..2..2..1..2....0..0..3..0..0..3....1..1..3..1..1..2....0..0..1..0..0..2

CROSSREFS

Row 6 of A252719.

Sequence in context: A300057 A197440 A261758 * A168355 A083255 A259283

Adjacent sequences: A252722 A252723 A252724 * A252726 A252727 A252728

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 20 2014

STATUS

approved