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A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero. 12

%I #4 Mar 30 2018 12:30:01

%S 0,1,0,1,2,0,2,2,5,0,3,8,5,13,0,5,18,26,15,34,0,8,50,84,74,48,89,0,13,

%T 128,309,468,200,155,233,0,21,338,1108,2036,2856,530,499,610,0,34,882,

%U 3979,10982,14016,17800,1394,1602,1597,0,55,2312,14314,53440,122232

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

%C Table starts

%C .0....1....1....2.......3........5..........8..........13............21

%C .0....2....2....8......18.......50........128.........338...........882

%C .0....5....5...26......84......309.......1108........3979.........14314

%C .0...13...15...74.....468.....2036......10982.......53440........271596

%C .0...34...48..200....2856....14016.....122232......813704.......6066698

%C .0...89..155..530...17800...100176....1366374....12824770.....133115004

%C .0..233..499.1394..110036...729297...15243860...204666568....2933712940

%C .0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404

%C .0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108

%H R. H. Hardin, <a href="/A301999/b301999.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 3*a(n-1) -a(n-2)

%F k=3: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3)

%F k=4: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3)

%F k=5: [order 11] for n>12

%F k=6: [order 32] for n>33

%F k=7: [order 52] for n>54

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2)

%F n=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

%F n=3: [order 20]

%e Some solutions for n=5 k=4

%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0

%e ..1..1..0..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0

%e ..1..0..1..0. .1..1..0..1. .1..1..1..1. .1..0..1..0. .1..1..0..0

%e ..0..1..0..1. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..1..1..1

%e ..0..0..1..1. .1..1..0..0. .0..1..0..0. .1..0..1..1. .0..0..1..1

%Y Column 2 is A001519.

%Y Row 1 is A000045(n-1).

%Y Row 2 is A175395(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 30 2018

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)