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A279158 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 7

%I

%S 0,0,0,2,0,2,2,4,4,2,5,12,20,12,5,8,30,72,72,30,8,15,72,255,428,255,

%T 72,15,26,162,874,2294,2294,874,162,26,46,356,2903,11932,20104,11932,

%U 2903,356,46,80,766,9336,60304,166552,166552,60304,9336,766,80,139,1616,29578

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ..0....0.....2.......2.........5...........8............15..............26

%C ..0....0.....4......12........30..........72...........162.............356

%C ..2....4....20......72.......255.........874..........2903............9336

%C ..2...12....72.....428......2294.......11932.........60304..........297092

%C ..5...30...255....2294.....20104......166552.......1331471........10508084

%C ..8...72...874...11932....166552.....2145788......26724386.......330704288

%C .15..162..2903...60304...1331471....26724386.....517476726.....10025433990

%C .26..356..9336..297092..10508084...330704288...10025433990....305617345164

%C .46..766.29578.1443498..81594334..4027185426..191191601644...9168921176076

%C .80.1616.92528.6930508.624717186.48341053840.3592564336954.270873567300596

%H R. H. Hardin, <a href="/A279158/b279158.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -12*a(n-4) +8*a(n-5) -4*a(n-6) +8*a(n-7)

%F k=3: [order 22] for n>23

%F k=4: [order 56] for n>57

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A006367(n-1).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Dec 06 2016

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)