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A252690
Number of (n+2) X (3+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.
1
148, 204, 134, 407, 291, 881, 727, 2067, 2067, 5331, 6491, 15287, 22035, 48395, 79207, 166155, 295755, 604671, 1132307, 2284763, 4405335, 8834267, 17313499, 34630815, 68480739, 136855275, 271964087, 543415691, 1082854443, 2163899807, 4318574515
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 7*a(n-3) + 2*a(n-4) + 6*a(n-5) + 14*a(n-6) - 20*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>10.
Empirical g.f.: x*(148 - 388*x - 386*x^2 + 1315*x^3 + 63*x^4 + 173*x^5 - 2930*x^6 + 1444*x^7 + 1192*x^8 - 608*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Dec 05 2018
EXAMPLE
Some solutions for n=4:
..0..1..1..2..2....0..0..1..0..0....0..0..1..1..0....0..0..1..1..0
..1..1..2..2..0....1..1..2..1..1....2..2..3..3..2....2..3..2..3..2
..1..2..2..0..0....1..1..2..1..1....0..0..1..1..0....2..3..2..3..2
..2..2..0..0..1....0..0..1..0..0....2..2..3..3..0....0..1..0..1..0
..2..0..0..1..1....1..1..2..1..1....0..0..1..1..2....0..1..0..1..0
..0..0..1..1..2....1..1..2..1..1....2..2..3..3..0....3..2..3..2..2
CROSSREFS
Column 3 of A252695.
Sequence in context: A308889 A214619 A061154 * A134212 A344409 A127028
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 20 2014
STATUS
approved