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A252861 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order 9

%I #4 Dec 23 2014 15:48:52

%S 117,279,279,684,432,684,1719,738,738,1719,4383,1296,1197,1296,4383,

%T 11286,2502,1962,1962,2502,11286,29241,4986,3582,3582,3582,4986,29241,

%U 76059,9936,6795,7002,7002,6795,9936,76059,198324,20052,12762,13590

%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order

%C Table starts

%C ....117...279...684...1719...4383...11286...29241...76059...198324...517923

%C ....279...432...738...1296...2502....4986....9936...20052....40770....82872

%C ....684...738..1197...1962...3582....6795...12762...24552....47367....91440

%C ...1719..1296..1962...3582...7002...13590...26766...52650...104796...207414

%C ...4383..2502..3582...7002..14229...28728...58644..119727...245016...501462

%C ..11286..4986..6795..13590..28728...60588..126306..266391...562293..1185867

%C ..29241..9936.12762..26766..58644..126306..275598..596250..1300068..2826126

%C ..76059.20052.24552..52650.119727..266391..596250.1334322..3002328..6731217

%C .198324.40770.47367.104796.245016..562293.1300068.3002328..6954849.16128072

%C .517923.82872.91440.207414.501462.1185867.2826126.6731217.16128072.38574297

%H R. H. Hardin, <a href="/A252861/b252861.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +a(n-4)

%F k=2: [order 9]

%F k=3: a(n) = 2*a(n-1) -a(n-5) +a(n-6) -2*a(n-7) +a(n-8) for n>10

%F k=4: [order 10] for n>12

%F k=5: [order 16] for n>18

%F k=6: [order 23] for n>26

%F k=7: [order 34] for n>36

%e Some solutions for n=4 k=4

%e ..0..1..1..2..1..2....0..1..0..1..0..1....0..1..0..0..2..0....0..1..1..2..2..0

%e ..2..1..1..0..0..1....1..1..0..0..1..1....2..0..0..1..1..2....2..0..2..0..2..2

%e ..2..2..0..2..0..2....0..0..1..0..1..0....2..1..1..0..1..0....0..0..2..2..0..0

%e ..1..1..0..0..1..1....1..0..0..2..2..1....1..0..1..1..2..2....0..2..0..2..0..2

%e ..1..2..1..2..1..2....1..2..1..2..2..0....1..1..0..0..2..0....1..0..0..1..1..2

%e ..2..1..1..2..2..1....2..2..1..1..0..1....2..0..0..1..1..2....1..2..1..2..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 23 2014

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Last modified February 23 08:25 EST 2024. Contains 370269 sequences. (Running on oeis4.)