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A297544 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.

%I A297544 #4 Dec 31 2017 15:03:57
%S A297544 1,1,1,1,2,1,1,11,4,1,1,24,35,7,1,1,38,93,88,14,1,1,105,197,275,461,
%T A297544 31,1,1,381,905,1233,2205,2050,69,1,1,1067,4617,10234,12161,13248,
%U A297544 8057,155,1,1,2676,17190,65363,205888,94647,67215,35640,354,1,1,7533,60751,355573
%N A297544 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.
%C A297544 Table starts
%C A297544 .1...1......1.......1........1...........1.............1..............1
%C A297544 .1...2.....11......24.......38.........105...........381...........1067
%C A297544 .1...4.....35......93......197.........905..........4617..........17190
%C A297544 .1...7.....88.....275.....1233.......10234.........65363.........355573
%C A297544 .1..14....461....2205....12161......205888.......2748026.......25141813
%C A297544 .1..31...2050...13248....94647.....3015179......67372651......916902295
%C A297544 .1..69...8057...67215...754342....45293985....1610981344....33425081735
%C A297544 .1.155..35640..401415..6315609...726450667...45496070039..1479214192234
%C A297544 .1.354.158090.2403621.51451261.11267743659.1204223924807.59920115456355
%H A297544 R. H. Hardin, <a href="/A297544/b297544.txt">Table of n, a(n) for n = 1..199</a>
%F A297544 Empirical for column k:
%F A297544 k=1: a(n) = a(n-1)
%F A297544 k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5)
%F A297544 k=3: [order 14]
%F A297544 k=4: [order 22]
%F A297544 k=5: [order 54]
%F A297544 Empirical for row n:
%F A297544 n=1: a(n) = a(n-1)
%F A297544 n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6)
%F A297544 n=3: [order 17]
%F A297544 n=4: [order 40]
%e A297544 Some solutions for n=5 k=4
%e A297544 ..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..1..0. .0..0..1..0
%e A297544 ..1..1..1..0. .0..1..1..1. .0..1..1..1. .0..1..1..1. .1..1..1..1
%e A297544 ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..0..0
%e A297544 ..0..0..1..1. .1..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..1
%e A297544 ..0..0..1..1. .0..1..0..0. .0..1..1..1. .0..1..1..1. .0..0..1..1
%Y A297544 Column 2 is A202973.
%K A297544 nonn,tabl
%O A297544 1,5
%A A297544 _R. H. Hardin_, Dec 31 2017