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A232047 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

%I A232047 #6 Jul 23 2025 06:50:12
%S A232047 2,2,4,4,7,8,7,15,21,16,12,34,80,65,32,21,79,318,446,200,64,37,184,
%T A232047 1315,3082,2477,616,128,65,426,5364,22063,29974,13752,1897,256,114,
%U A232047 984,21680,153562,377676,290672,76375,5842,512,200,2274,87452,1060850,4588174
%N A232047 T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
%C A232047 Table starts
%C A232047 ....2.....2........4..........7...........12..............21................37
%C A232047 ....4.....7.......15.........34...........79.............184...............426
%C A232047 ....8....21.......80........318.........1315............5364.............21680
%C A232047 ...16....65......446.......3082........22063..........153562...........1060850
%C A232047 ...32...200.....2477......29974.......377676.........4588174..........55505057
%C A232047 ...64...616....13752.....290672......6430408.......136134243........2882322121
%C A232047 ..128..1897....76375....2821630....109609484......4041385884......149582129861
%C A232047 ..256..5842...424115...27382537...1868028342....119990644449.....7766282047395
%C A232047 ..512.17991..2355221..265752221..31836538191...3562337669985...403179428472169
%C A232047 .1024.55405.13079032.2579134666.542586883485.105762437152368.20931014633412316
%H A232047 R. H. Hardin, <a href="/A232047/b232047.txt">Table of n, a(n) for n = 1..478</a>
%F A232047 Empirical for column k:
%F A232047 k=1: a(n) = 2*a(n-1)
%F A232047 k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3)
%F A232047 k=3: a(n) = 4*a(n-1) +9*a(n-2) -a(n-3) -6*a(n-4) for n>5
%F A232047 k=4: [order 8] for n>9
%F A232047 k=5: [order 14] for n>15
%F A232047 k=6: [order 24] for n>26
%F A232047 k=7: [order 44] for n>47
%F A232047 Empirical for row n:
%F A232047 n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
%F A232047 n=2: a(n) = 4*a(n-1) -6*a(n-2) +7*a(n-3) -6*a(n-4) +3*a(n-5) -a(n-6) -a(n-7) for n>8
%F A232047 n=3: [order 15] for n>18
%F A232047 n=4: [order 33] for n>36
%F A232047 n=5: [order 78] for n>84
%e A232047 Some solutions for n=4 k=4
%e A232047 ..0..0..0..1....0..0..0..1....1..0..0..0....0..0..0..0....1..1..0..0
%e A232047 ..1..0..1..1....0..0..1..0....0..0..0..0....1..0..0..0....0..0..1..0
%e A232047 ..0..0..0..1....0..1..0..0....0..1..0..0....1..1..1..0....0..1..0..1
%e A232047 ..1..0..0..0....1..0..0..1....1..0..0..1....1..1..0..0....0..0..1..1
%Y A232047 Column 1 is A000079
%Y A232047 Column 2 is A218836
%Y A232047 Row 1 is A005251(n+2)
%K A232047 nonn,tabl
%O A232047 1,1
%A A232047 _R. H. Hardin_, Nov 17 2013