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A231227 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231227 #6 Jul 23 2025 06:19:38
%S A231227 1,2,2,3,4,3,6,8,8,6,11,17,21,17,11,22,45,54,54,45,22,43,103,185,182,
%T A231227 185,103,43,86,264,552,812,812,552,264,86,171,676,1799,2962,4298,2962,
%U A231227 1799,676,171,342,1724,5900,12179,19935,19935,12179,5900,1724,342,683,4501
%N A231227 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231227 Table starts
%C A231227 ...1....2.....3......6.......11........22.........43.........86........171
%C A231227 ...2....4.....8.....17.......45.......103........264........676.......1724
%C A231227 ...3....8....21.....54......185.......552.......1799.......5900......19185
%C A231227 ...6...17....54....182......812......2962......12179......50196.....205057
%C A231227 ..11...45...185....812.....4298.....19935.....102113.....524113....2687777
%C A231227 ..22..103...552...2962....19935....117178.....748665....4870988...31483476
%C A231227 ..43..264..1799..12179...102113....748665....5930126...48317804..390225796
%C A231227 ..86..676..5900..50196...524113...4870988...48317804..495739986.5038813008
%C A231227 .171.1724.19185.205057..2687777..31483476..390225796.5038813008
%C A231227 .342.4501.63834.864270.14197596.210326324.3267809753
%H A231227 R. H. Hardin, <a href="/A231227/b231227.txt">Table of n, a(n) for n = 1..144</a>
%F A231227 Empirical for column k:
%F A231227 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F A231227 k=2: [order 11]
%F A231227 k=3: [order 13]
%F A231227 k=4: [order 96]
%e A231227 Some solutions for n=5 k=4
%e A231227 ..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..0....0..0..0..0..0..0
%e A231227 ..0..0..1..1..0..0....0..0..0..0..1..1....0..0..1..1..0..0....0..0..1..1..0..0
%e A231227 ..1..1..1..1..1..1....1..1..1..1..0..0....1..1..1..1..1..1....1..1..1..1..1..1
%e A231227 ..1..1..1..1..1..1....1..1..1..1..0..0....1..1..1..1..1..1....1..1..1..1..1..1
%e A231227 ..0..0..1..1..2..2....0..0..0..0..1..1....0..0..1..1..0..0....2..2..1..1..0..0
%e A231227 ..0..0..0..2..2..2....0..0..0..0..1..1....0..0..0..0..0..0....2..2..2..0..0..0
%e A231227 ..0..0..0..2..2..2....0..0..0..0..1..1....0..0..0..0..0..0....2..2..2..0..0..0
%Y A231227 Column 1 is A005578
%K A231227 nonn,tabl
%O A231227 1,2
%A A231227 _R. H. Hardin_, Nov 05 2013