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A304270 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 5 or 8 king-move adjacent elements, with upper left element zero.

%I A304270 #4 May 09 2018 10:14:57
%S A304270 1,2,2,3,1,3,5,3,3,5,8,5,6,5,8,13,7,10,10,7,13,21,13,19,21,19,13,21,
%T A304270 34,23,37,50,50,37,23,34,55,37,67,116,146,116,67,37,55,89,63,124,259,
%U A304270 404,404,259,124,63,89,144,109,235,601,1074,1246,1074,601,235,109,144,233
%N A304270 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 5 or 8 king-move adjacent elements, with upper left element zero.
%C A304270 Table starts
%C A304270 ..1..2...3....5....8....13.....21......34......55.......89.......144.......233
%C A304270 ..2..1...3....5....7....13.....23......37......63......109.......183.......309
%C A304270 ..3..3...6...10...19....37.....67.....124.....235......436.......808......1513
%C A304270 ..5..5..10...21...50...116....259.....601....1397.....3196......7359.....17016
%C A304270 ..8..7..19...50..146...404...1074....2990....8316....22660.....62314....172244
%C A304270 .13.13..37..116..404..1246...3788...12342...39252...122156....388150...1234248
%C A304270 .21.23..67..259.1074..3788..13767...53839..201274...741275...2806825..10575217
%C A304270 .34.37.124..601.2990.12342..53839..252509.1118021..4901568..22174589..99427544
%C A304270 .55.63.235.1397.8316.39252.201274.1118021.5755625.29475545.156881417.822798993
%H A304270 R. H. Hardin, <a href="/A304270/b304270.txt">Table of n, a(n) for n = 1..1012</a>
%F A304270 Empirical for column k:
%F A304270 k=1: a(n) = a(n-1) +a(n-2)
%F A304270 k=2: a(n) = a(n-1) +2*a(n-3) for n>4
%F A304270 k=3: a(n) = a(n-1) +3*a(n-3) for n>4
%F A304270 k=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +a(n-4) -3*a(n-5) -3*a(n-6) for n>7
%F A304270 k=5: [order 9] for n>10
%F A304270 k=6: [order 12] for n>13
%F A304270 k=7: [order 24] for n>25
%e A304270 Some solutions for n=5 k=4
%e A304270 ..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
%e A304270 ..0..0..0..0. .1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A304270 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0
%e A304270 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A304270 ..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
%Y A304270 Column 1 is A000045(n+1).
%Y A304270 Column 2 is A003229(n-1).
%K A304270 nonn,tabl
%O A304270 1,2
%A A304270 _R. H. Hardin_, May 09 2018