cp's OEIS Frontend

A232281 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

%I A232281 #6 Jul 23 2025 07:14:47
%S A232281 3,3,9,9,35,27,22,199,104,81,51,1066,1672,341,243,121,6019,23055,
%T A232281 18117,1189,729,292,32301,293426,604133,184115,4040,2187,704,174400,
%U A232281 3476318,17145989,14477600,1774344,13560,6561,1691,944500,43029161,450287974
%N A232281 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.
%C A232281 Table starts
%C A232281 .....3......3..........9............22...............51.................121
%C A232281 .....9.....35........199..........1066.............6019...............32301
%C A232281 ....27....104.......1672.........23055...........293426.............3476318
%C A232281 ....81....341......18117........604133.........17145989...........450287974
%C A232281 ...243...1189.....184115......14477600........906702319.........52334662011
%C A232281 ...729...4040....1774344.....340593196......47260154104.......6001447087200
%C A232281 ..2187..13560...17764558....8229274953....2527067273698.....706877889324298
%C A232281 ..6561..45803..178471267..198816273957..135096346014359...83179007080796381
%C A232281 .19683.155131.1771400531.4771778176334.7180729990183315.9733054114073214077
%H A232281 R. H. Hardin, <a href="/A232281/b232281.txt">Table of n, a(n) for n = 1..127</a>
%F A232281 Empirical for column k:
%F A232281 k=1: a(n) = 3*a(n-1)
%F A232281 k=2: [order 11] for n>12
%F A232281 k=3: [order 35] for n>36
%F A232281 Empirical for row n:
%F A232281 n=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
%F A232281 n=2: [order 10]
%F A232281 n=3: [order 52] for n>53
%e A232281 Some solutions for n=3 k=4
%e A232281 ..0..0..0..1....2..0..0..0....0..2..0..0....2..2..1..1....0..1..0..2
%e A232281 ..1..0..1..2....2..0..0..0....0..0..0..0....1..1..2..2....2..0..0..0
%e A232281 ..0..0..0..0....0..2..1..2....0..0..0..0....1..1..1..1....0..2..0..0
%Y A232281 Column 1 is A000244
%Y A232281 Column 2 is A231645
%Y A232281 Row 1 is A202882 for n>1
%K A232281 nonn,tabl
%O A232281 1,1
%A A232281 _R. H. Hardin_, Nov 22 2013