A207111 - OEIS

%I #5 Mar 31 2012 12:37:15

%S 2,4,4,6,16,6,9,36,36,8,13,81,98,64,10,18,169,271,200,100,12,25,324,

%T 677,643,350,144,14,34,625,1504,1835,1271,556,196,16,46,1156,3399,

%U 4534,4047,2239,826,256,18,62,2116,7220,11511,10898,7837,3641,1168,324,20,83,3844

%N T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 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...98..271...677..1504...3399...7220...15184...31664....64749...132543

%C ..8..64..200..643..1835..4534..11511..27012...62814..144676...325111...733469

%C .10.100..350.1271..4047.10898..30415..77326..194952..486102..1177409..2870021

%C .12.144..556.2239..7837.22714..68737.187054..505040.1346150..3472283..9030485

%C .14.196..826.3641.13863.42874.139341.402498.1153962.3259098..8878431.24420005

%C .16.256.1168.5581.22931.75198.260597.794118.2402578.7142988.20426983.59031673

%H R. H. Hardin, <a href="/A207111/b207111.txt">Table of n, a(n) for n = 1..612</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) = (4/3)*n^3 + 8*n^2 - (10/3)*n

%F k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1

%F k=5: a(n) = (7/60)*n^5 + (8/3)*n^4 + (185/12)*n^3 + (19/3)*n^2 - (218/15)*n + 3

%F k=6: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6

%F k=7: a(n) = (1/280)*n^7 + (7/45)*n^6 + (47/15)*n^5 + (206/9)*n^4 + (4111/120)*n^3 - (1037/45)*n^2 - (4493/210)*n + 9

%e Some solutions for n=4 k=3

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

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

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

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

%Y Column 2 is A016742

%Y Row 1 is A171861(n+1)

%Y Row 2 is A207025

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 15 2012