A239599 - OEIS

%I #4 Mar 22 2014 06:02:46

%S 2,4,3,10,3,4,24,15,4,7,56,64,31,4,10,132,244,187,82,5,15,312,1030,

%T 1310,643,177,7,24,736,4303,9806,8773,1737,458,8,35,1736,17923,76769,

%U 128347,38824,7461,1071,11,54,4096,75264,611126,1991329,1031560,282333,24946

%N 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 Table starts

%C ..2..4....10.....24.......56........132.........312.........736........1736

%C ..3..3....15.....64......244.......1030........4303.......17923.......75264

%C ..4..4....31....187.....1310.......9806.......76769......611126.....4929897

%C ..7..4....82....643.....8773.....128347.....1991329....31686730...510551001

%C .10..5...177...1737....38824....1031560....30460289...944810972.30050150163

%C .15..7...458...7461...282333...12509870...681399736.40483561185

%C .24..8..1071..24946..1583770..120511910.11135057785

%C .35.11..2150..78667..8002162.1104844380

%C .54.12..5209.313003.56967196

%C .83.16.11204.946740

%H R. H. Hardin, <a href="/A239599/b239599.txt">Table of n, a(n) for n = 1..95</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3)

%F k=2: a(n) = a(n-2) +a(n-5) for n>6

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) +2*a(n-3)

%F n=2: [order 44] for n>47

%e Some solutions for n=4 k=4

%e ..3..0..0..2....3..0..2..0....3..0..0..0....3..0..0..2....3..0..0..2

%e ..2..3..0..0....3..2..2..2....2..3..0..2....2..3..2..2....2..3..2..0

%e ..3..2..2..0....2..1..0..0....3..2..2..2....3..2..0..2....3..2..0..0

%e ..2..1..2..0....2..1..2..0....2..3..2..0....2..1..2..0....2..3..2..2

%Y Column 1 is A159288(n+1)

%Y Row 1 is A052912

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 22 2014