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A239599 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 one 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 A239599 #6 Jun 02 2025 09:29:31
%S A239599 2,4,3,10,3,4,24,15,4,7,56,64,31,4,10,132,244,187,82,5,15,312,1030,
%T A239599 1310,643,177,7,24,736,4303,9806,8773,1737,458,8,35,1736,17923,76769,
%U A239599 128347,38824,7461,1071,11,54,4096,75264,611126,1991329,1031560,282333,24946
%N A239599 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 one 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 A239599 Table starts
%C A239599 ..2..4....10.....24.......56........132.........312.........736........1736
%C A239599 ..3..3....15.....64......244.......1030........4303.......17923.......75264
%C A239599 ..4..4....31....187.....1310.......9806.......76769......611126.....4929897
%C A239599 ..7..4....82....643.....8773.....128347.....1991329....31686730...510551001
%C A239599 .10..5...177...1737....38824....1031560....30460289...944810972.30050150163
%C A239599 .15..7...458...7461...282333...12509870...681399736.40483561185
%C A239599 .24..8..1071..24946..1583770..120511910.11135057785
%C A239599 .35.11..2150..78667..8002162.1104844380
%C A239599 .54.12..5209.313003.56967196
%C A239599 .83.16.11204.946740
%H A239599 R. H. Hardin, <a href="/A239599/b239599.txt">Table of n, a(n) for n = 1..95</a>
%F A239599 Empirical for column k:
%F A239599 k=1: a(n) = a(n-2) +2*a(n-3)
%F A239599 k=2: a(n) = a(n-2) +a(n-5) for n>6
%F A239599 Empirical for row n:
%F A239599 n=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A239599 n=2: [order 44] for n>47
%e A239599 Some solutions for n=4 k=4
%e A239599 ..3..0..0..2....3..0..2..0....3..0..0..0....3..0..0..2....3..0..0..2
%e A239599 ..2..3..0..0....3..2..2..2....2..3..0..2....2..3..2..2....2..3..2..0
%e A239599 ..3..2..2..0....2..1..0..0....3..2..2..2....3..2..0..2....3..2..0..0
%e A239599 ..2..1..2..0....2..1..2..0....2..3..2..0....2..1..2..0....2..3..2..2
%Y A239599 Column 1 is A159288(n+1)
%Y A239599 Row 1 is A052912
%K A239599 nonn,tabl
%O A239599 1,1
%A A239599 _R. H. Hardin_, Mar 22 2014