A207403 - OEIS

%I #5 Mar 31 2012 12:37:17

%S 2,4,4,6,16,6,9,36,36,8,12,81,102,64,10,16,144,289,216,100,12,20,256,

%T 612,729,390,144,14,25,400,1296,1782,1521,636,196,16,30,625,2340,4356,

%U 4212,2809,966,256,18,36,900,4225,8910,11664,8692,4761,1392,324,20,42,1296

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

%C Table starts

%C ..2...4....6....9....12.....16.....20.....25......30......36.......42.......49

%C ..4..16...36...81...144....256....400....625.....900....1296.....1764.....2401

%C ..6..36..102..289...612...1296...2340...4225....6890...11236....17066....25921

%C ..8..64..216..729..1782...4356...8910..18225...33210...60516...101598...170569

%C .10.100..390.1521..4212..11664..26676..61009..123006..248004...456666...840889

%C .12.144..636.2809..8692..26896..68060.172225..380970..842724..1690038..3389281

%C .14.196..966.4761.16284..55696.154580.429025.1033590.2490084..5404650.11730625

%C .16.256.1392.7569.28362.106276.321110.970225.2529480.6594624.15405432.35988001

%H R. H. Hardin, <a href="/A207403/b207403.txt">Table of n, a(n) for n = 1..1512</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) = 2*n^3 + 6*n^2 - 2*n

%F k=4: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1

%F k=5: a(n) = (1/3)*n^5 + 3*n^4 + (28/3)*n^3 + 7*n^2 - (29/3)*n + 2

%F k=6: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4

%F k=7: a(n) = (1/36)*n^7 + (4/9)*n^6 + (53/18)*n^5 + (91/9)*n^4 + (589/36)*n^3 + (31/9)*n^2 - (58/3)*n + 6

%e Some solutions for n=4 k=3

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

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

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

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

%Y Column 2 is A016742

%Y Column 3 is A086113

%Y Row 1 is A002620(n+2)

%Y Row 2 is A030179(n+2)

%Y Row 3 is A207118

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 17 2012