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A231263 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231263 #6 Jul 23 2025 06:21:23
%S A231263 2,3,6,4,15,22,7,32,89,86,12,83,304,547,342,23,211,1253,2982,3381,
%T A231263 1366,44,557,5109,19503,29366,20911,5462,87,1471,21894,126851,302121,
%U A231263 289230,129329,21846,172,3909,94234,866396,3130708,4670875,2848550,799835,87382
%N A231263 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231263 Table starts
%C A231263 ......2........3..........4............7.............12...............23
%C A231263 ......6.......15.........32...........83............211..............557
%C A231263 .....22.......89........304.........1253...........5109............21894
%C A231263 .....86......547.......2982........19503.........126851...........866396
%C A231263 ....342.....3381......29366.......302121........3130708.........34170727
%C A231263 ...1366....20911.....289230......4670875.......77333664.......1350570015
%C A231263 ...5462...129329....2848550.....72212345.....1911322499......53369789699
%C A231263 ..21846...799835...28054534...1116538567....47238533054....2108712981800
%C A231263 ..87382..4946509..276301638..17264116873..1167469879103...83318930054700
%C A231263 .349526.30591143.2721223974.266940042371.28853204049176.3292096503338981
%H A231263 R. H. Hardin, <a href="/A231263/b231263.txt">Table of n, a(n) for n = 1..161</a>
%F A231263 Empirical for column k:
%F A231263 k=1: a(n) = 5*a(n-1) -4*a(n-2)
%F A231263 k=2: a(n) = 10*a(n-1) -29*a(n-2) +36*a(n-3) -16*a(n-4)
%F A231263 k=3: [order 7]
%F A231263 k=4: [order 12]
%F A231263 k=5: [order 32]
%F A231263 k=6: [order 67] for n>68
%F A231263 Empirical for row n:
%F A231263 n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F A231263 n=2: [order 9]
%F A231263 n=3: [order 27] for n>28
%e A231263 Some solutions for n=3 k=4
%e A231263 ..0..0..0..0..1....0..0..0..0..0....0..0..1..1..1....0..0..1..1..1
%e A231263 ..0..0..0..1..0....0..0..0..0..0....0..1..0..0..0....0..1..1..1..1
%e A231263 ..1..1..1..0..0....0..1..1..1..0....1..0..2..2..1....2..2..0..0..2
%e A231263 ..1..1..1..1..1....1..1..1..0..0....0..2..2..1..1....2..0..0..2..2
%Y A231263 Column 1 is A047849
%Y A231263 Row 1 is A023105(n+1)
%K A231263 nonn,tabl
%O A231263 1,1
%A A231263 _R. H. Hardin_, Nov 06 2013