A269201 - OEIS

%I #4 Feb 20 2016 10:29:14

%S 4,16,16,60,180,64,216,1284,1740,256,756,9612,25572,15540,1024,2592,

%T 68052,400428,471492,132300,4096,8748,472044,5877228,15289548,8314020,

%U 1090740,16384,29160,3212820,84310620,463790340,555862380,142233732

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

%C Table starts

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

%C ......16........180...........1284..............9612................68052

%C ......64.......1740..........25572............400428..............5877228

%C .....256......15540.........471492..........15289548............463790340

%C ....1024.....132300........8314020.........555862380..........34838403756

%C ....4096....1090740......142233732.......19558138380........2532677348772

%C ...16384....8787660.....2380537188......672230393004......179867149105740

%C ...65536...69580980....39186271044....22702294138188....12551707872624132

%C ..262144..543538380...636703584804...756261535626732...864008559706781292

%C .1048576.4200069300.10237337586180.24917784636315276.58827234014669683044

%H R. H. Hardin, <a href="/A269201/b269201.txt">Table of n, a(n) for n = 1..161</a>

%F Empirical for column k:

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

%F k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3

%F k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5

%F k=4: [order 6] for n>7

%F k=5: [order 20] for n>21

%F k=6: [order 42] for n>43

%F Empirical for row n:

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

%F n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)

%F n=3: [order 8]

%F n=4: [order 20]

%F n=5: [order 52] for n>53

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000302.

%Y Column 2 is A269103.

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 20 2016