|
%I #7 Oct 13 2021 15:04:38
%S 2,4,4,6,16,6,9,36,36,8,15,81,90,64,10,25,225,225,168,100,12,40,625,
%T 825,441,270,144,14,64,1600,3025,1995,729,396,196,16,104,4096,9240,
%U 9025,3915,1089,546,256,18,169,10816,28224,30400,21025,6765,1521,720,324,20,273
%N T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C Table starts
%C ..2...4...6....9....15.....25.....40......64......104......169.......273
%C ..4..16..36...81...225....625...1600....4096....10816....28561.....74529
%C ..6..36..90..225...825...3025...9240...28224....93912...312481....997815
%C ..8..64.168..441..1995...9025..30400..102400...403520..1590121...5746377
%C .10.100.270..729..3915..21025..75400..270400..1223560..5536609..21791133
%C .12.144.396.1089..6765..42025.157440..589824..3005184.15311569..64177113
%C .14.196.546.1521.10725..75625.292600.1132096..6404216.36228361.159389139
%C .16.256.720.2025.15975.126025.499840.1982464.12318592.76545001.350003745
%H R. H. Hardin, <a href="/A207599/b207599.txt">Table of n, a(n) for n = 1..1250</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) = 36*n^2 - 36*n + 9
%F k=5: a(n) = 30*n^3 + 15*n^2 - 45*n + 15
%F k=6: a(n) = 25*n^4 + 50*n^3 - 25*n^2 - 50*n + 25
%F k=7: a(n) = 120*n^4 + 40*n^3 - 200*n^2 + 80*n
%e Some solutions for n=4 k=3
%e ..1..0..1....1..0..0....0..0..1....1..0..0....1..1..0....1..0..0....1..1..0
%e ..1..1..0....0..0..1....0..0..1....0..1..1....1..0..1....1..0..0....0..1..1
%e ..1..0..0....0..0..1....0..0..1....0..0..1....1..0..0....1..0..0....0..1..1
%e ..1..0..0....0..0..1....0..0..1....0..0..1....1..0..0....1..0..0....0..1..1
%Y Column 2 is A016742.
%Y Column 3 is A152746.
%Y Column 4 is A016946(n-1).
%Y Row 1 is A006498(n+2).
%Y Row 2 is A189145(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Feb 19 2012
| 