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A281715 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A281715 #4 Jan 28 2017 13:45:51
%S A281715 1,1,2,1,3,4,2,7,4,8,3,14,8,6,16,5,29,38,14,9,32,8,61,90,97,17,14,64,
%T A281715 13,126,305,294,245,22,22,128,21,265,902,1410,937,631,30,35,256,34,
%U A281715 553,2710,5781,6417,3166,1625,43,56,512,55,1162,8376,23798,37781,29849,10738,4234
%N A281715 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C A281715 Table starts
%C A281715 ...1..1..1.....2......3........5.........8..........13...........21
%C A281715 ...2..3..7....14.....29.......61.......126.........265..........553
%C A281715 ...4..4..8....38.....90......305.......902........2710.........8376
%C A281715 ...8..6.14....97....294.....1410......5781.......23798.......103034
%C A281715 ..16..9.17...245....937.....6417.....37781......214045......1321909
%C A281715 ..32.14.22...631...3166....29849....252867.....1987696.....17241122
%C A281715 ..64.22.30..1625..10738...142023...1721319....18779855....230037168
%C A281715 .128.35.43..4234..37285...677045..11737418...178547832...3076165855
%C A281715 .256.56.64.11017.129586..3244671..80326035..1704685390..41247350230
%C A281715 .512.90.98.28652.452042.15605137.550174620.16297041786.554236736742
%H A281715 R. H. Hardin, <a href="/A281715/b281715.txt">Table of n, a(n) for n = 1..199</a>
%F A281715 Empirical for column k:
%F A281715 k=1: a(n) = 2*a(n-1)
%F A281715 k=2: a(n) = 2*a(n-1) -a(n-3) for n>4
%F A281715 k=3: a(n) = 2*a(n-1) -a(n-3) for n>6
%F A281715 k=4: [order 15] for n>16
%F A281715 k=5: [order 24] for n>28
%F A281715 Empirical for row n:
%F A281715 n=1: a(n) = a(n-1) +a(n-2) for n>3
%F A281715 n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5)
%F A281715 n=3: [order 20] for n>21
%F A281715 n=4: [order 72] for n>73
%e A281715 Some solutions for n=4 k=4
%e A281715 ..0..0..1..0. .0..0..1..0. .0..1..0..1. .0..0..1..1. .0..0..0..1
%e A281715 ..1..1..0..1. .1..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..1..1
%e A281715 ..1..1..1..0. .1..1..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..1
%e A281715 ..1..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .1..1..0..0
%Y A281715 Column 1 is A000079(n-1).
%Y A281715 Column 2 is A001611(n+1).
%Y A281715 Row 1 is A000045(n-1).
%K A281715 nonn,tabl
%O A281715 1,3
%A A281715 _R. H. Hardin_, Jan 28 2017