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A241397 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A241397 #6 Jun 02 2025 10:07:36
%S A241397 2,2,3,4,5,4,6,9,13,7,8,23,29,28,10,14,44,85,97,64,15,20,93,201,480,
%T A241397 340,142,24,30,204,689,1657,2780,1156,318,35,48,368,1929,8697,15339,
%U A241397 17211,4068,726,54,70,761,4068,31654,129985,160947,102782,14763,1634,83,108
%N A241397 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
%C A241397 Table starts
%C A241397 ..2....2......4........6..........8..........14..........20.........30
%C A241397 ..3....5......9.......23.........44..........93.........204........368
%C A241397 ..4...13.....29.......85........201.........689........1929.......4068
%C A241397 ..7...28.....97......480.......1657........8697.......31654......92204
%C A241397 .10...64....340.....2780......15339......129985......667050....2949778
%C A241397 .15..142...1156....17211.....160947.....2234804....18589398..134190457
%C A241397 .24..318...4068...102782....1622867....39781828...541660724.7518340973
%C A241397 .35..726..14763...645484...18627122...821631365.21331876978
%C A241397 .54.1634..52950..3936420..196990531.16108803423
%C A241397 .83.3695.190950.24633252.2356216195
%H A241397 R. H. Hardin, <a href="/A241397/b241397.txt">Table of n, a(n) for n = 1..112</a>
%F A241397 Empirical for column k:
%F A241397 k=1: a(n) = a(n-2) +2*a(n-3)
%F A241397 k=2: [order 38]
%F A241397 Empirical for row n:
%F A241397 n=1: a(n) = a(n-2) +2*a(n-3)
%F A241397 n=2: [order 22] for n>23
%e A241397 Some solutions for n=4 k=4
%e A241397 ..3..2..3..3....3..2..2..2....2..3..3..2....2..3..3..2....2..3..3..2
%e A241397 ..1..2..1..2....2..1..0..0....2..1..2..0....2..3..2..2....1..3..1..2
%e A241397 ..3..2..0..0....3..1..2..0....3..0..0..2....2..0..0..3....1..2..0..2
%e A241397 ..1..0..0..0....3..2..0..0....2..0..1..0....2..1..1..3....3..2..2..2
%Y A241397 Column 1 is A159288(n+1)
%Y A241397 Row 1 is A239851
%K A241397 nonn,tabl
%O A241397 1,1
%A A241397 _R. H. Hardin_, Apr 20 2014