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A207305 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207305 #7 Jul 22 2025 20:16:46
%S A207305 2,4,4,6,16,6,9,36,36,8,13,81,98,64,10,19,169,271,200,100,12,28,361,
%T A207305 665,643,350,144,14,41,784,1675,1759,1271,556,196,16,60,1681,4344,
%U A207305 4939,3773,2239,826,256,18,88,3600,11081,14446,11497,7093,3641,1168,324,20,129
%N A207305 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207305 Table starts
%C A207305 ..2...4....6....9....13....19.....28......41......60.......88......129
%C A207305 ..4..16...36...81...169...361....784....1681....3600.....7744....16641
%C A207305 ..6..36...98..271...665..1675...4344...11081...28136....71908...183709
%C A207305 ..8..64..200..643..1759..4939..14446...41505..118266...339548...975493
%C A207305 .10.100..350.1271..3773.11497..36868..116117..361408..1134028..3564401
%C A207305 .12.144..556.2239..7093.23091..79802..271023..906448..3057442.10340359
%C A207305 .14.196..826.3641.12169.41893.154228..558557.1985288..7118528.25615229
%C A207305 .16.256.1168.5581.19515.70537.274288.1050811.3937294.14887794.56536529
%H A207305 R. H. Hardin, <a href="/A207305/b207305.txt">Table of n, a(n) for n = 1..480</a>
%F A207305 Empirical for column k:
%F A207305 k=1: a(n) = 2*n
%F A207305 k=2: a(n) = 4*n^2
%F A207305 k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
%F A207305 k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
%F A207305 k=5: a(n) = (8/3)*n^4 + (49/3)*n^3 + (16/3)*n^2 - (43/3)*n + 3
%F A207305 k=6: a(n) = (4/15)*n^5 + (45/4)*n^4 + (199/6)*n^3 - (73/4)*n^2 - (373/30)*n + 5
%F A207305 k=7: a(n) = (187/60)*n^5 + (153/4)*n^4 + (455/12)*n^3 - (249/4)*n^2 + (209/30)*n + 4
%e A207305 Some solutions for n=4 k=3
%e A207305 ..1..1..1....0..1..0....1..1..0....0..0..1....1..1..0....0..1..0....1..0..0
%e A207305 ..1..1..1....1..1..0....0..0..1....0..0..1....1..0..0....0..1..0....0..0..1
%e A207305 ..1..1..1....0..1..0....1..1..1....0..0..1....1..0..0....0..1..0....1..0..0
%e A207305 ..1..1..1....1..1..0....1..1..1....0..0..1....1..0..0....0..1..0....0..0..1
%Y A207305 Column 2 is A016742
%Y A207305 Column 3 is A207106
%Y A207305 Column 4 is A207107
%Y A207305 Row 1 is A000930(n+3)
%Y A207305 Row 2 is A207170
%K A207305 nonn,tabl
%O A207305 1,1
%A A207305 _R. H. Hardin_ Feb 16 2012