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A296128 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.

%I A296128 #4 Dec 05 2017 06:51:21
%S A296128 1,1,1,1,5,1,1,9,9,1,1,13,18,13,1,1,33,30,30,33,1,1,69,107,74,107,69,
%T A296128 1,1,121,265,287,287,265,121,1,1,253,553,841,2098,841,553,253,1,1,529,
%U A296128 1505,2463,9344,9344,2463,1505,529,1,1,1013,3852,7953,35733,54286,35733,7953
%N A296128 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.
%C A296128 Table starts
%C A296128 .1...1....1.....1......1........1.........1..........1...........1............1
%C A296128 .1...5....9....13.....33.......69.......121........253.........529.........1013
%C A296128 .1...9...18....30....107......265.......553.......1505........3852.........8922
%C A296128 .1..13...30....74....287......841......2463.......7953.......24428........74660
%C A296128 .1..33..107...287...2098.....9344.....35733.....182881......859151......3752449
%C A296128 .1..69..265...841...9344....54286....263489....1867837....11720327.....67180741
%C A296128 .1.121..553..2463..35733...263489...1810441...16855693...138016847...1087543621
%C A296128 .1.253.1505..7953.182881..1867837..16855693..227074899..2614792001..28292082465
%C A296128 .1.529.3852.24428.859151.11720327.138016847.2614792001.41069612676.599261543598
%H A296128 R. H. Hardin, <a href="/A296128/b296128.txt">Table of n, a(n) for n = 1..287</a>
%F A296128 Empirical for column k:
%F A296128 k=1: a(n) = a(n-1)
%F A296128 k=2: a(n) = a(n-1) +4*a(n-3)
%F A296128 k=3: a(n) = 2*a(n-1) -a(n-2) +8*a(n-3) -7*a(n-4) +2*a(n-5) -2*a(n-6)
%F A296128 k=4: [order 9]
%F A296128 k=5: [order 39]
%e A296128 Some solutions for n=5 k=4
%e A296128 ..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..0..0..0. .0..1..1..0
%e A296128 ..0..1..0..0. .0..1..1..0. .1..0..0..1. .0..0..0..1. .0..0..1..0
%e A296128 ..0..0..0..0. .0..0..0..0. .0..1..0..1. .0..0..1..1. .0..0..0..0
%e A296128 ..1..0..0..0. .1..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..0..0
%e A296128 ..1..1..0..0. .1..1..0..0. .0..0..1..0. .1..1..0..0. .0..0..0..0
%Y A296128 Column 2 is A089977(n+1).
%Y A296128 Column 3 is A183444.
%K A296128 nonn,tabl
%O A296128 1,5
%A A296128 _R. H. Hardin_, Dec 05 2017