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A204381 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order 9

%I

%S 33,51,51,78,48,78,113,54,54,113,182,63,61,63,182,286,88,75,75,88,286,

%T 439,128,98,87,98,128,439,710,193,139,111,111,139,193,710,1128,300,

%U 205,153,136,153,205,300,1128,1775,470,310,217,176,176,217,310,470,1775,2873

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order

%C Table starts

%C ..33..51..78.113.182.286.439.710.1128.1775.2873.4628.7422.12063.19589.31772

%C ..51..48..54..63..88.128.193.300..470..747.1196.1920.3093..4992..8062.13031

%C ..78..54..61..75..98.139.205.310..481..759.1206.1931.3105..5002..8073.13043

%C .113..63..75..87.111.153.217.323..495..771.1219.1945.3117..5015..8087.13055

%C .182..88..98.111.136.176.241.348..518..795.1244.1968.3141..5040..8110.13079

%C .286.128.139.153.176.217.283.388..559..837.1284.2009.3183..5080..8151.13121

%C .439.193.205.217.241.283.347.453..625..901.1349.2075.3247..5145..8217.13185

%C .710.300.310.323.348.388.453.560..730.1007.1456.2180.3353..5252..8322.13291

%H R. H. Hardin, <a href="/A204381/b204381.txt">Table of n, a(n) for n = 1..1103</a>

%F Empirical for column k:

%F k=1: a(n)=3*a(n-1)-2*a(n-2)-2*a(n-4)+2*a(n-5)+3*a(n-6)-6*a(n-7)+3*a(n-8)-a(n-11)+2*a(n-12)-a(n-13)-a(n-14)+2*a(n-15)-a(n-16)

%F k=2..7: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8

%e Some solutions for n=3 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 14 2012

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)