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A231663 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors 8

%I #4 Nov 12 2013 12:58:06

%S 3,3,3,9,15,9,22,93,93,22,51,458,1197,458,51,121,2163,13434,13434,

%T 2163,121,292,10789,144465,345519,144465,10789,292,704,53813,1607589,

%U 8300390,8300390,1607589,53813,704,1691,265397,17962078,206363144,434469343

%N T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors

%C Table starts

%C ....3.......3..........9............22...............51.................121

%C ....3......15.........93...........458.............2163...............10789

%C ....9......93.......1197.........13434...........144465.............1607589

%C ...22.....458......13434........345519..........8300390...........206363144

%C ...51....2163.....144465.......8300390........434469343.........23632808750

%C ..121...10789....1607589.....206363144......23632808750.......2825994465190

%C ..292...53813...17962078....5175246459....1304771142134.....344368908016123

%C ..704..265397..199451319..128866716238...71426776678405...41555342706134920

%C .1691.1311447.2215334132.3207643017150.3902799543486962.5000894272327355414

%H R. H. Hardin, <a href="/A231663/b231663.txt">Table of n, a(n) for n = 1..161</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6

%F k=2: [order 15]

%F k=3: [order 57]

%e Some solutions for n=3 k=4

%e ..0..0..0..2....2..1..0..0....0..0..1..1....0..0..1..0....1..1..0..2

%e ..0..2..0..0....1..1..0..0....0..0..1..0....0..0..0..0....1..0..0..1

%e ..2..2..0..2....2..2..0..2....1..0..0..0....0..0..1..0....2..0..1..1

%Y Column 1 is A202882 for n>1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 12 2013

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)