A269194 - OEIS

%I #4 Feb 20 2016 09:46:22

%S 4,16,16,60,108,60,216,708,708,216,756,4476,9284,4476,756,2592,27684,

%T 115452,115452,27684,2592,8748,168252,1399612,2817548,1399612,168252,

%U 8748,29160,1008804,16629436,67134380,67134380,16629436,1008804,29160

%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

%C Table starts

%C ......4........16...........60.............216................756

%C .....16.......108..........708............4476..............27684

%C .....60.......708.........9284..........115452............1399612

%C ....216......4476.......115452.........2817548...........67134380

%C ....756.....27684......1399612........67134380.........3159954052

%C ...2592....168252.....16629436......1567933676.......145995171708

%C ...8748...1008804....194596516.....36068275268......6648192704604

%C ..29160...5983164...2249848972....819789099172....299224791093196

%C ..96228..35170980..25758552060..18452018423420..13339889117822420

%C .314928.205214268.292530733516.411983259384452.590022908205332548

%H R. H. Hardin, <a href="/A269194/b269194.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -9*a(n-2)

%F k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5

%F k=3: [order 8] for n>9

%F k=4: [order 16] for n>17

%F k=5: [order 40] for n>41

%e Some solutions for n=3 k=4

%e ..0..1..1..3. .0..0..2..2. .2..3..1..3. .1..3..1..1. .2..3..2..1

%e ..0..1..3..1. .2..0..0..2. .2..3..1..3. .1..1..1..3. .2..2..3..3

%e ..1..3..1..1. .2..0..2..0. .3..3..1..0. .0..3..1..3. .3..2..3..2

%Y Column 1 is A120926(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 20 2016