A281344 - OEIS

%I #4 Jan 20 2017 14:15:14

%S 1,2,2,4,8,4,8,25,25,8,16,85,68,85,16,32,286,193,193,286,32,64,969,

%T 544,607,544,969,64,128,3281,1539,1892,1892,1539,3281,128,256,11114,

%U 4355,5868,6256,5868,4355,11114,256,512,37649,12332,18189,19700,19700,18189

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ...1......2.....4......8......16......32.......64......128.......256.......512

%C ...2......8....25.....85.....286.....969.....3281....11114.....37649....127541

%C ...4.....25....68....193.....544....1539.....4355....12332.....34907.....98797

%C ...8.....85...193....607....1892....5868....18189....56154....173062....534110

%C ..16....286...544...1892....6256...19700....60540...185696....569832...1754082

%C ..32....969..1539...5868...19700...63168...198619...620828...1944159...6105081

%C ..64...3281..4355..18189...60540..198619...639142..2039214...6489813..20683647

%C .128..11114.12332..56154..185696..620828..2039214..6658147..21625033..70229690

%C .256..37649.34907.173062..569832.1944159..6489813.21625033..71489598.235986575

%C .512.127541.98797.534110.1754082.6105081.20683647.70229690.235986575.791069059

%H R. H. Hardin, <a href="/A281344/b281344.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

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

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

%F k=3: [order 9] for n>10

%F k=4: [order 18] for n>21

%F k=5: [order 49] for n>55

%F k=6: [order 98] for n>107

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 20 2017