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%I #4 Apr 09 2018 09:09:28
%S 1,2,2,3,3,4,5,3,4,8,8,5,11,6,16,13,7,15,9,9,32,21,13,21,28,14,14,64,
%T 34,23,52,36,48,21,22,128,55,37,118,80,90,89,28,35,256,89,63,220,235,
%U 199,184,163,37,56,512,144,109,408,541,689,458,376,297,51,90,1024,233,183
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1..2..3...5....8...13....21.....34......55......89......144.......233
%C ...2..3..3...5....7...13....23.....37......63.....109......183.......309
%C ...4..4.11..15...21...52...118....220.....408.....852.....1764......3460
%C ...8..6..9..28...36...80...235....541....1115....2554.....6095.....13920
%C ..16..9.14..48...90..199...689...2125....5410...13908....39850....114503
%C ..32.14.21..89..184..458..1784...7182...22544...67096...220654....775150
%C ..64.22.28.163..376.1088..4558..23944...95681..344525..1302832...5550086
%C .128.35.37.297..832.2651.12324..82857..414880.1775176..7735877..39371229
%C .256.56.51.544.1744.6257.32336.282857.1748514.8778929.44362463.272701915
%H R. H. Hardin, <a href="/A302515/b302515.txt">Table of n, a(n) for n = 1..511</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) -a(n-3)
%F k=3: a(n) = a(n-1) +a(n-4) for n>7
%F k=4: a(n) = a(n-1) +2*a(n-3) +2*a(n-4) -a(n-6) -a(n-7) for n>10
%F k=5: a(n) = a(n-1) +6*a(n-3) +2*a(n-5) -12*a(n-6) -4*a(n-7) +8*a(n-9) for n>11
%F k=6: a(n) = a(n-1) +6*a(n-3) +5*a(n-4) +3*a(n-5) -8*a(n-6) -6*a(n-7) -3*a(n-8) for n>12
%F k=7: [order 15] for n>21
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +2*a(n-3) for n>5
%F n=3: a(n) = a(n-1) +2*a(n-3) +4*a(n-4) for n>7
%F n=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +5*a(n-4) -a(n-5) -5*a(n-6) -4*a(n-7) for n>10
%F n=5: [order 13] for n>17
%F n=6: [order 23] for n>29
%F n=7: [order 50] for n>55
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
%e ..1..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..0..1
%e ..1..0..1..0. .0..0..1..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
%e ..1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e ..1..0..0..0. .1..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A001611(n+1).
%Y Row 1 is A000045(n+1).
%Y Row 2 is A003227(n-1) for n>2.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 09 2018