A207024 - OEIS

%I #7 Mar 26 2023 10:31:04

%S 2,4,4,6,16,6,9,36,36,8,13,81,90,64,10,18,169,252,168,100,12,25,324,

%T 624,558,270,144,14,34,625,1350,1586,1035,396,196,16,46,1156,3025,

%U 3726,3315,1719,546,256,18,62,2116,6256,9450,8280,6123,2646,720,324,20,83,3844

%N T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Table starts

%C ..2...4...6....9....13....18.....25.....34......46......62.......83......111

%C ..4..16..36...81...169...324....625...1156....2116....3844.....6889....12321

%C ..6..36..90..252...624..1350...3025...6256...12788...25792....50630....99012

%C ..8..64.168..558..1586..3726...9450..21318...47518..104470...220531...464202

%C .10.100.270.1035..3315..8280..23400..56814..136114..322834...725005..1627260

%C .12.144.396.1719..6123.16038..49925.129302..329498..836938..1984447..4716834

%C .14.196.546.2646.10374.28224..95900.263228..707756.1914436..4765030.11929281

%C .16.256.720.3852.16484.46260.170300.492932.1389476.3984244.10362550.27202659

%H R. H. Hardin, <a href="/A207024/b207024.txt">Table of n, a(n) for n = 1..1984</a>

%F Empirical for column k:

%F k=1: a(n) = 2*n

%F k=2: a(n) = 4*n^2

%F k=3: a(n) = 12*n^2 - 6*n

%F k=4: a(n) = 6*n^3 + (27/2)*n^2 - (21/2)*n

%F k=5: a(n) = (13/6)*n^4 + 13*n^3 + (52/3)*n^2 - (39/2)*n

%F k=6: a(n) = (33/4)*n^4 + (45/2)*n^3 + (75/4)*n^2 - (63/2)*n

%F k=7: a(n) = (55/24)*n^5 + (75/4)*n^4 + (275/8)*n^3 + (75/4)*n^2 - (295/6)*n

%e Some solutions for n=4, k=3

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

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

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

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

%Y Column 2 is A016742.

%Y Column 3 is A152746.

%Y Row 1 is A171861(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 14 2012