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A303719 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.

%I A303719 #5 Apr 29 2018 10:57:13
%S A303719 1,2,2,3,1,3,5,3,3,5,8,5,5,5,8,13,7,8,8,7,13,21,13,14,17,14,13,21,34,
%T A303719 23,24,36,36,24,23,34,55,37,40,76,81,76,40,37,55,89,63,68,161,169,169,
%U A303719 161,68,63,89,144,109,116,349,361,343,361,349,116,109,144,233,183,196,749
%N A303719 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.
%C A303719 Table starts
%C A303719 ..1..2...3...5....8...13...21....34....55....89....144....233....377.....610
%C A303719 ..2..1...3...5....7...13...23....37....63...109....183....309....527.....893
%C A303719 ..3..3...5...8...14...24...40....68...116...196....332....564....956....1620
%C A303719 ..5..5...8..17...36...76..161...349...749..1604...3449...7412..15912...34177
%C A303719 ..8..7..14..36...81..169..361...784..1681..3600...7744..16641..35721...76729
%C A303719 .13.13..24..76..169..343..741..1618..3451..7390..15924..34201..73387..157681
%C A303719 .21.23..40.161..361..741.1592..3469..7416.15880..34193..73457.157645..338676
%C A303719 .34.37..68.349..784.1618.3469..7551.16159.34602..74481.160024.343450..737809
%C A303719 .55.63.116.749.1681.3451.7416.16159.34546.73974.159281.342185.734359.1577656
%H A303719 R. H. Hardin, <a href="/A303719/b303719.txt">Table of n, a(n) for n = 1..6123</a>
%F A303719 Empirical for diagonal:
%F A303719 Diagonal: [linear recurrence of order 15] for n>18
%F A303719 Empirical for column k:
%F A303719 k=1: a(n) = a(n-1) +a(n-2)
%F A303719 k=2: a(n) = a(n-1) +2*a(n-3) for n>4
%F A303719 k=3: a(n) = a(n-1) +2*a(n-3) for n>4
%F A303719 k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
%F A303719 k=5: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
%F A303719 k=6: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
%F A303719 k=7: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
%e A303719 Some solutions for n=5 k=4
%e A303719 ..0..0..1..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A303719 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..0
%e A303719 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A303719 ..1..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
%e A303719 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0
%Y A303719 Column 1 is A000045(n+1).
%Y A303719 Column 2 is A003229(n-1).
%K A303719 nonn,tabl
%O A303719 1,2
%A A303719 _R. H. Hardin_, Apr 29 2018