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A280069 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A280069 #4 Dec 25 2016 06:41:52
%S A280069 1,1,1,1,1,1,2,2,2,2,3,4,5,4,3,5,9,15,15,9,5,8,19,39,52,39,19,8,13,41,
%T A280069 104,170,170,104,41,13,21,88,281,603,790,603,281,88,21,34,189,771,
%U A280069 2157,3729,3729,2157,771,189,34,55,406,2122,7777,17468,23564,17468,7777,2122
%N A280069 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C A280069 Table starts
%C A280069 ..1...1....1......2.......3........5.........8..........13...........21
%C A280069 ..1...1....2......4.......9.......19........41..........88..........189
%C A280069 ..1...2....5.....15......39......104.......281.........771.........2122
%C A280069 ..2...4...15.....52.....170......603......2157........7777........28195
%C A280069 ..3...9...39....170.....790.....3729.....17468.......82769.......394904
%C A280069 ..5..19..104....603....3729....23564....145485......915505......5786757
%C A280069 ..8..41..281...2157...17468...145485...1188839.....9934415.....83159859
%C A280069 .13..88..771...7777...82769...915505...9934415...110266512...1225662273
%C A280069 .21.189.2122..28195..394904..5786757..83159859..1225662273..18113056960
%C A280069 .34.406.5858.102429.1890877.36671797.698377561.13669391105.268403179093
%H A280069 R. H. Hardin, <a href="/A280069/b280069.txt">Table of n, a(n) for n = 1..263</a>
%F A280069 Empirical for column k:
%F A280069 k=1: a(n) = a(n-1) +a(n-2) for n>3
%F A280069 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) for n>4
%F A280069 k=3: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) +5*a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7) for n>9
%F A280069 k=4: [order 15] for n>18
%F A280069 k=5: [order 35] for n>40
%F A280069 k=6: [order 87] for n>91
%e A280069 Some solutions for n=4 k=4
%e A280069 ..0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A280069 ..0..1..1..1. .0..1..1..0. .1..1..0..0. .0..0..0..0. .0..0..0..1
%e A280069 ..0..0..0..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..1..1..1
%e A280069 ..0..0..0..1. .1..1..0..0. .1..1..1..0. .1..1..1..1. .1..1..1..1
%Y A280069 Column 1 is A000045(n-1).
%Y A280069 Column 2 is A078039(n-2).
%K A280069 nonn,tabl
%O A280069 1,7
%A A280069 _R. H. Hardin_, Dec 25 2016