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A207111 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.

%I A207111 #7 Jul 22 2025 20:01:52
%S A207111 2,4,4,6,16,6,9,36,36,8,13,81,98,64,10,18,169,271,200,100,12,25,324,
%T A207111 677,643,350,144,14,34,625,1504,1835,1271,556,196,16,46,1156,3399,
%U A207111 4534,4047,2239,826,256,18,62,2116,7220,11511,10898,7837,3641,1168,324,20,83,3844
%N A207111 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 A207111 Table starts
%C A207111 ..2...4....6....9....13....18.....25.....34......46......62.......83......111
%C A207111 ..4..16...36...81...169...324....625...1156....2116....3844.....6889....12321
%C A207111 ..6..36...98..271...677..1504...3399...7220...15184...31664....64749...132543
%C A207111 ..8..64..200..643..1835..4534..11511..27012...62814..144676...325111...733469
%C A207111 .10.100..350.1271..4047.10898..30415..77326..194952..486102..1177409..2870021
%C A207111 .12.144..556.2239..7837.22714..68737.187054..505040.1346150..3472283..9030485
%C A207111 .14.196..826.3641.13863.42874.139341.402498.1153962.3259098..8878431.24420005
%C A207111 .16.256.1168.5581.22931.75198.260597.794118.2402578.7142988.20426983.59031673
%H A207111 R. H. Hardin, <a href="/A207111/b207111.txt">Table of n, a(n) for n = 1..612</a>
%F A207111 Empirical for column k:
%F A207111 k=1: a(n) = 2*n
%F A207111 k=2: a(n) = 4*n^2
%F A207111 k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
%F A207111 k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
%F A207111 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 A207111 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 A207111 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 A207111 Some solutions for n=4 k=3
%e A207111 ..0..1..0....0..0..1....1..0..0....1..0..0....1..1..1....0..1..0....1..1..0
%e A207111 ..1..0..1....0..1..0....1..0..1....0..0..1....1..1..1....0..1..0....0..0..1
%e A207111 ..0..0..1....0..0..1....1..0..1....1..0..1....1..1..1....0..1..0....0..1..0
%e A207111 ..1..0..1....0..1..0....1..0..1....0..0..1....1..1..1....0..1..0....0..1..0
%Y A207111 Column 2 is A016742
%Y A207111 Row 1 is A171861(n+1)
%Y A207111 Row 2 is A207025
%K A207111 nonn,tabl
%O A207111 1,1
%A A207111 _R. H. Hardin_ Feb 15 2012