A265887 - OEIS

%I #4 Dec 17 2015 17:03:57

%S 3,4,4,6,12,6,8,16,16,8,12,32,68,32,12,16,64,128,128,64,16,24,128,384,

%T 664,384,128,24,32,256,1024,2048,2048,1024,256,32,48,512,3072,8192,

%U 13672,8192,3072,512,48,64,1024,8192,32768,65536,65536,32768,8192,1024,64,96

%N T(n,k)=Number of nXk 0..2 arrays with the sum of the absolute differences of each element with its horizontal and vertical neighbors equal to the number of neighbors.

%C Table starts

%C ..3....4.....6.......8.......12.........16..........24............32

%C ..4...12....16......32.......64........128.........256...........512

%C ..6...16....68.....128......384.......1024........3072..........8192

%C ..8...32...128.....664.....2048.......8192.......32768........131072

%C .12...64...384....2048....13672......65536......393216.......2097152

%C .16..128..1024....8192....65536.....560512.....4194304......33554432

%C .24..256..3072...32768...393216....4194304....51483264.....536870912

%C .32..512..8192..131072..2097152...33554432...536870912....8726974464

%C .48.1024.24576..524288.12582912..268435456..6442450944..137438953472

%C .64.2048.65536.2097152.67108864.2147483648.68719476736.2199023255552

%H R. H. Hardin, <a href="/A265887/b265887.txt">Table of n, a(n) for n = 1..684</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 8*a(n-2) for n>5

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

%F k=5: a(n) = 32*a(n-2) for n>7

%F k=6: a(n) = 8*a(n-1) for n>7

%F k=7: a(n) = 128*a(n-2) for n>9

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A029744(n+2).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 17 2015