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A303525 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303525 #4 Apr 25 2018 12:41:08
%S A303525 1,2,2,3,3,4,5,11,6,8,8,21,18,10,16,13,31,37,39,21,32,21,113,80,103,
%T A303525 95,42,64,34,363,286,359,340,246,86,128,55,813,916,1875,1758,1115,687,
%U A303525 179,256,89,1751,2532,8676,13031,9225,4112,2023,370,512,144,5001,7477,36072
%N A303525 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303525 Table starts
%C A303525 ...1...2....3.....5.......8........13.........21...........34............55
%C A303525 ...2...3...11....21......31.......113........363..........813..........1751
%C A303525 ...4...6...18....37......80.......286........916.........2532..........7477
%C A303525 ...8..10...39...103.....359......1875.......8676........36072........166784
%C A303525 ..16..21...95...340....1758.....13031......87730.......569770.......4036330
%C A303525 ..32..42..246..1115....9225....102779....1052163.....10663440.....122173279
%C A303525 ..64..86..687..4112...56046....965150...15768709....258412452....4730074082
%C A303525 .128.179.2023.16640..366415...9961980..260078546...6835357512..199276300520
%C A303525 .256.370.6126.71025.2519399.109395622.4544413190.190464446456.8858057538977
%H A303525 R. H. Hardin, <a href="/A303525/b303525.txt">Table of n, a(n) for n = 1..180</a>
%F A303525 Empirical for column k:
%F A303525 k=1: a(n) = 2*a(n-1)
%F A303525 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A303525 k=3: [order 12] for n>15
%F A303525 k=4: [order 47] for n>49
%F A303525 Empirical for row n:
%F A303525 n=1: a(n) = a(n-1) +a(n-2)
%F A303525 n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
%F A303525 n=3: [order 20] for n>21
%F A303525 n=4: [order 58] for n>60
%e A303525 Some solutions for n=5 k=4
%e A303525 ..0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0
%e A303525 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..0..0
%e A303525 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .1..1..1..0
%e A303525 ..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1. .1..0..1..0
%e A303525 ..0..1..1..1. .0..1..1..0. .1..0..1..0. .0..1..1..1. .1..0..1..0
%Y A303525 Column 1 is A000079(n-1).
%Y A303525 Column 2 is A240513.
%Y A303525 Row 1 is A000045(n+1).
%Y A303525 Row 2 is A302310.
%K A303525 nonn,tabl
%O A303525 1,2
%A A303525 _R. H. Hardin_, Apr 25 2018