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A280554 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A280554 #4 Jan 05 2017 08:27:57
%S A280554 0,0,0,0,0,0,1,9,9,1,2,34,50,34,2,6,87,144,144,87,6,13,194,325,382,
%T A280554 325,194,13,29,400,670,832,832,670,400,29,60,790,1316,1666,1764,1666,
%U A280554 1316,790,60,122,1511,2502,3182,3438,3438,3182,2502,1511,122,241,2830,4654
%N A280554 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C A280554 Table starts
%C A280554 ...0....0....0.....1.....2.....6....13.....29.....60....122....241....468
%C A280554 ...0....0....9....34....87...194...400....790...1511...2830...5213...9484
%C A280554 ...0....9...50...144...325...670..1316...2502...4654...8521..15412..27612
%C A280554 ...1...34..144...382...832..1666..3182...5886..10680..19122..33920..59754
%C A280554 ...2...87..325...832..1764..3438..6386..11506..20389..35757..62317.108150
%C A280554 ...6..194..670..1666..3438..6502.11697..20440..35226..60300.102974.175746
%C A280554 ..13..400.1316..3182..6386.11697.20334..34360..57389..95548.159360.266756
%C A280554 ..29..790.2502..5886.11506.20440.34360..56102..90614.146264.237392.388378
%C A280554 ..60.1511.4654.10680.20389.35226.57389..90614.141398.220709.347310.553046
%C A280554 .122.2830.8521.19122.35757.60300.95548.146264.220709.332810.506359.781682
%H A280554 R. H. Hardin, <a href="/A280554/b280554.txt">Table of n, a(n) for n = 1..391</a>
%F A280554 Empirical for column k:
%F A280554 k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
%F A280554 k=2: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>9
%F A280554 k=3: a(n) = 5*a(n-1) -7*a(n-2) -2*a(n-3) +10*a(n-4) -2*a(n-5) -5*a(n-6) +a(n-7) +a(n-8) for n>10
%F A280554 k=4: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>11
%F A280554 k=5: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
%F A280554 k=6: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
%F A280554 k=7: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>12
%e A280554 Some solutions for n=4 k=4
%e A280554 ..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
%e A280554 ..1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..1. .1..0..1..1
%e A280554 ..0..1..1..0. .1..0..1..0. .0..0..1..0. .1..0..1..0. .0..1..0..0
%e A280554 ..1..0..1..0. .0..0..1..0. .1..1..0..1. .1..1..0..0. .0..1..0..1
%Y A280554 Column 1 is A055243(n-4).
%Y A280554 Column 2 is A279128.
%K A280554 nonn,tabl
%O A280554 1,8
%A A280554 _R. H. Hardin_, Jan 05 2017