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A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303314 #4 Apr 21 2018 12:48:28
%S A303314 1,2,2,3,3,4,5,3,4,8,8,5,12,6,16,13,7,17,11,9,32,21,13,24,36,19,14,64,
%T A303314 34,23,67,50,74,34,22,128,55,37,158,128,139,165,53,35,256,89,63,298,
%U A303314 439,410,349,361,83,56,512,144,109,595,1085,1799,1221,853,783,136,90,1024,233
%N A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303314 Table starts
%C A303314 ...1..2...3....5....8....13.....21......34.......55........89........144
%C A303314 ...2..3...3....5....7....13.....23......37.......63.......109........183
%C A303314 ...4..4..12...17...24....67....158.....298......595......1337.......2863
%C A303314 ...8..6..11...36...50...128....439....1085.....2431......6452......17455
%C A303314 ..16..9..19...74..139...410...1799....5907....16494.....53290.....184915
%C A303314 ..32.14..34..165..349..1221...7096...30280...102683....403872....1783894
%C A303314 ..64.22..53..361..853..3453..26184..148313...618149...2955145...16591424
%C A303314 .128.35..83..783.2180.10223.100128..746323..3851318..22515378..159560449
%C A303314 .256.56.136.1710.5525.30247.387892.3784002.23967605.171306353.1539204838
%H A303314 R. H. Hardin, <a href="/A303314/b303314.txt">Table of n, a(n) for n = 1..511</a>
%F A303314 Empirical for column k:
%F A303314 k=1: a(n) = 2*a(n-1)
%F A303314 k=2: a(n) = 2*a(n-1) -a(n-3)
%F A303314 k=3: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7
%F A303314 k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10
%F A303314 k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12
%F A303314 k=6: [order 8] for n>11
%F A303314 k=7: [order 20] for n>23
%F A303314 Empirical for row n:
%F A303314 n=1: a(n) = a(n-1) +a(n-2)
%F A303314 n=2: a(n) = a(n-1) +2*a(n-3) for n>5
%F A303314 n=3: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7
%F A303314 n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11
%F A303314 n=5: [order 12] for n>16
%F A303314 n=6: [order 23] for n>28
%F A303314 n=7: [order 46] for n>51
%e A303314 Some solutions for n=5 k=4
%e A303314 ..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
%e A303314 ..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1
%e A303314 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A303314 ..0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1
%e A303314 ..0..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1
%Y A303314 Column 1 is A000079(n-1).
%Y A303314 Column 2 is A001611(n+1).
%Y A303314 Row 1 is A000045(n+1).
%Y A303314 Row 2 is A003229(n-1) for n>2.
%K A303314 nonn,tabl
%O A303314 1,2
%A A303314 _R. H. Hardin_, Apr 21 2018