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A281056 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%I A281056 #4 Jan 13 2017 16:58:56
%S A281056 0,0,0,0,1,0,1,6,6,0,2,34,68,29,0,6,104,239,376,122,0,13,251,618,1022,
%T A281056 1492,468,0,29,535,1403,2452,3416,4988,1686,0,60,1076,2828,5400,7803,
%U A281056 10112,15028,5807,0,122,2090,5482,10570,16875,22106,27635,42252,19338,0
%N A281056 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C A281056 Table starts
%C A281056 .0.....0......0......1......2.......6......13......29......60......122......241
%C A281056 .0.....1......6.....34....104.....251.....535....1076....2090.....3956.....7353
%C A281056 .0.....6.....68....239....618....1403....2828....5482...10342....19136....34907
%C A281056 .0....29....376...1022...2452....5400...10570...19892...36616....66354...118926
%C A281056 .0...122...1492...3416...7803...16875...32370...59669..107693...191953...339219
%C A281056 .0...468...4988..10112..22106...46610...87995..159317..282552...495655...864369
%C A281056 .0..1686..15028..27635..58005..119205..221212..394884..689397..1191475..2050466
%C A281056 .0..5807..42252..71419.144283..288527..526340..926077.1596265..2721514..4625355
%C A281056 .0.19338.113076.177320.344972..671451.1201939.2084979.3549039..5982952.10051523
%C A281056 .0.62731.291660.426696.800225.1515524.2661939.4546633.7645715.12749511.21211441
%H A281056 R. H. Hardin, <a href="/A281056/b281056.txt">Table of n, a(n) for n = 1..338</a>
%F A281056 Empirical for column k:
%F A281056 k=1: a(n) = a(n-1)
%F A281056 k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6)
%F A281056 k=3: a(n) = 5*a(n-1) -6*a(n-2) -4*a(n-3) +8*a(n-4) for n>6
%F A281056 k=4: [order 12] for n>14
%F A281056 k=5: [order 13] for n>16
%F A281056 k=6: [order 18] for n>21
%F A281056 k=7: [order 19] for n>23
%F A281056 Empirical for row n:
%F A281056 n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
%F A281056 n=2: [order 8] for n>14
%F A281056 n=3: [same order 8] for n>15
%F A281056 n=4: [order 9] for n>17
%F A281056 n=5: [same order 9] for n>18
%F A281056 n=6: [same order 9] for n>19
%F A281056 n=7: [same order 9] for n>20
%e A281056 Some solutions for n=4 k=4
%e A281056 ..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
%e A281056 ..1..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .1..0..1..1
%e A281056 ..0..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..0..1. .1..0..0..1
%e A281056 ..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..0..1..1. .1..0..1..0
%Y A281056 Row 1 is A055243(n-4).
%K A281056 nonn,tabl
%O A281056 1,8
%A A281056 _R. H. Hardin_, Jan 13 2017