A281955 - OEIS

%I #4 Feb 03 2017 08:27:02

%S 1,2,2,4,8,4,8,30,30,8,16,112,133,112,16,32,420,587,587,420,32,64,

%T 1576,2559,3389,2559,1576,64,128,5912,11251,19089,19089,11251,5912,

%U 128,256,22176,49293,111354,130416,111354,49293,22176,256,512,83184,216274

%N T(n,k)=Number of nXk 0..1 arrays with no element unequal to more than four 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

%C ...2......8......30.......112........420........1576..........5912

%C ...4.....30.....133.......587.......2559.......11251.........49293

%C ...8....112.....587......3389......19089......111354........640778

%C ..16....420....2559.....19089.....130416......944967.......6763599

%C ..32...1576...11251....111354.....944967.....8606584......77540974

%C ..64...5912...49293....640778....6763599....77540974.....882270370

%C .128..22176..216274...3716432...48984359...705601833...10123006858

%C .256..83184..948407..21502354..354789627..6439770627..116604534792

%C .512.312032.4159753.124531091.2573699813.58888042279.1345813812696

%H R. H. Hardin, <a href="/A281955/b281955.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

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

%F k=3: [order 10] for n>12

%F k=4: [order 28] for n>32

%F k=5: [order 69] for n>73

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 03 2017