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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.

%I A279158 #4 Dec 06 2016 22:57:57
%S A279158 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 A279158 72,15,26,162,874,2294,2294,874,162,26,46,356,2903,11932,20104,11932,
%U A279158 2903,356,46,80,766,9336,60304,166552,166552,60304,9336,766,80,139,1616,29578
%N 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.
%C A279158 Table starts
%C A279158 ..0....0.....2.......2.........5...........8............15..............26
%C A279158 ..0....0.....4......12........30..........72...........162.............356
%C A279158 ..2....4....20......72.......255.........874..........2903............9336
%C A279158 ..2...12....72.....428......2294.......11932.........60304..........297092
%C A279158 ..5...30...255....2294.....20104......166552.......1331471........10508084
%C A279158 ..8...72...874...11932....166552.....2145788......26724386.......330704288
%C A279158 .15..162..2903...60304...1331471....26724386.....517476726.....10025433990
%C A279158 .26..356..9336..297092..10508084...330704288...10025433990....305617345164
%C A279158 .46..766.29578.1443498..81594334..4027185426..191191601644...9168921176076
%C A279158 .80.1616.92528.6930508.624717186.48341053840.3592564336954.270873567300596
%H A279158 R. H. Hardin, <a href="/A279158/b279158.txt">Table of n, a(n) for n = 1..180</a>
%F A279158 Empirical for column k:
%F A279158 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F A279158 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 A279158 k=3: [order 22] for n>23
%F A279158 k=4: [order 56] for n>57
%e A279158 Some solutions for n=4 k=4
%e A279158 ..0..1..0..1. .0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..0
%e A279158 ..0..0..1..0. .0..0..1..0. .1..0..1..1. .0..1..0..1. .0..0..1..1
%e A279158 ..1..1..0..1. .1..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..0..0
%e A279158 ..0..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..0..1. .0..1..0..1
%Y A279158 Column 1 is A006367(n-1).
%K A279158 nonn,tabl
%O A279158 1,4
%A A279158 _R. H. Hardin_, Dec 06 2016