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A302427 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302427 #4 Apr 07 2018 17:21:57
%S A302427 1,2,2,3,3,4,5,9,6,8,8,17,11,10,16,13,25,21,21,21,32,21,65,38,42,51,
%T A302427 42,64,34,185,88,83,148,93,86,128,55,385,188,235,372,362,207,179,256,
%U A302427 89,649,377,532,1359,992,879,517,370,512,144,1489,735,1250,4223,4231,2503,2447
%N A302427 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302427 Table starts
%C A302427 ...1...2....3....5.....8.....13.....21......34.......55........89........144
%C A302427 ...2...3....9...17....25.....65....185.....385......649......1489.......3929
%C A302427 ...4...6...11...21....38.....88....188.....377......735......1557.......3288
%C A302427 ...8..10...21...42....83....235....532....1250.....2839......6972......16274
%C A302427 ..16..21...51..148...372...1359...4223...12765....36991....120577.....379049
%C A302427 ..32..42...93..362...992...4231..14764...53851...182216....685166....2496115
%C A302427 ..64..86..207..879..2503..12527..48037..204549...775916...3358602...13687791
%C A302427 .128.179..517.2447..7611..49454.227283.1171867..5110314..27366139..134037982
%C A302427 .256.370.1007.6306.21321.179252.940829.6104653.30957683.207165078.1213329113
%H A302427 R. H. Hardin, <a href="/A302427/b302427.txt">Table of n, a(n) for n = 1..286</a>
%F A302427 Empirical for column k:
%F A302427 k=1: a(n) = 2*a(n-1)
%F A302427 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A302427 k=3: a(n) = a(n-1) +10*a(n-3) -8*a(n-4) for n>9
%F A302427 k=4: [order 42] for n>43
%F A302427 k=5: [order 21] for n>24
%F A302427 Empirical for row n:
%F A302427 n=1: a(n) = a(n-1) +a(n-2)
%F A302427 n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
%F A302427 n=3: [order 18] for n>19
%F A302427 n=4: [order 68] for n>69
%e A302427 Some solutions for n=5 k=4
%e A302427 ..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A302427 ..0..1..0..1. .0..1..0..1. .1..1..0..1. .0..1..0..0. .1..1..0..1
%e A302427 ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A302427 ..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..0
%e A302427 ..1..0..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
%Y A302427 Column 1 is A000079(n-1).
%Y A302427 Column 2 is A240513.
%Y A302427 Row 1 is A000045(n+1).
%Y A302427 Row 2 is A302164.
%K A302427 nonn,tabl
%O A302427 1,2
%A A302427 _R. H. Hardin_, Apr 07 2018