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A302728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302728 #4 Apr 12 2018 10:54:32
%S A302728 0,1,0,1,3,0,2,7,10,0,3,10,22,23,0,5,27,29,83,61,0,8,45,74,89,301,162,
%T A302728 0,13,98,162,287,353,1079,421,0,21,193,363,689,1307,941,4064,1103,0,
%U A302728 34,379,782,1723,4505,4491,3316,15183,2890,0,55,778,1766,4491,16265,20842,17828
%N A302728 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302728 Table starts
%C A302728 .0....1.....1.....2......3.......5........8........13........21.........34
%C A302728 .0....3.....7....10.....27......45.......98.......193.......379........778
%C A302728 .0...10....22....29.....74.....162......363.......782......1766.......3953
%C A302728 .0...23....83....89....287.....689.....1723......4491.....10433......28009
%C A302728 .0...61...301...353...1307....4505....16265.....46773....136935.....481479
%C A302728 .0..162..1079...941...4491...20842....89121....286746...1022779....4520360
%C A302728 .0..421..4064..3316..17828..104969...532511...1932168...7608792...40495097
%C A302728 .0.1103.15183.12016..80293..623549..4281120..17200486..81226394..547173278
%C A302728 .0.2890.55012.34060.304958.3195095.26823700.120221024.683140749.5901256655
%H A302728 R. H. Hardin, <a href="/A302728/b302728.txt">Table of n, a(n) for n = 1..220</a>
%F A302728 Empirical for column k:
%F A302728 k=1: a(n) = a(n-1)
%F A302728 k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
%F A302728 k=3: [order 16]
%F A302728 k=4: [order 72] for n>73
%F A302728 Empirical for row n:
%F A302728 n=1: a(n) = a(n-1) +a(n-2)
%F A302728 n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
%F A302728 n=3: [order 16] for n>18
%F A302728 n=4: [order 68] for n>69
%e A302728 Some solutions for n=5 k=4
%e A302728 ..0..0..0..0. .0..1..1..1. .0..0..1..1. .0..1..0..1. .0..1..1..0
%e A302728 ..1..0..1..0. .1..0..0..0. .0..0..1..1. .1..0..1..0. .0..0..0..0
%e A302728 ..0..1..0..1. .1..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..0
%e A302728 ..1..0..1..0. .0..1..1..1. .0..1..1..0. .1..0..1..0. .0..0..0..0
%e A302728 ..1..1..1..1. .1..0..0..0. .1..0..0..1. .0..0..0..0. .0..1..1..0
%Y A302728 Column 2 is A185828.
%Y A302728 Column 4 is A302274.
%Y A302728 Row 1 is A000045(n-1).
%Y A302728 Row 2 is A302279.
%Y A302728 Row 3 is A302280.
%K A302728 nonn,tabl
%O A302728 1,5
%A A302728 _R. H. Hardin_, Apr 12 2018