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%I #4 Apr 04 2014 17:09:36
%S 1,1,2,1,5,2,1,7,12,4,1,9,32,50,4,1,11,62,258,120,8,1,13,118,954,1232,
%T 493,8,1,15,206,3064,8656,10291,1184,16,1,17,351,9075,50756,142016,
%U 48826,4863,16,1,19,568,27120,263816,1568581,1314136,405404,11684,32,1,21,882
%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 two plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..1.....1........1..........1............1.............1.............1
%C ..2.....5........7..........9...........11............13............15
%C ..2....12.......32.........62..........118...........206...........351
%C ..4....50......258........954.........3064..........9075.........27120
%C ..4...120.....1232.......8656........50756........263816.......1378418
%C ..8...493....10291.....142016......1568581......14958462.....138422394
%C ..8..1184....48826....1314136.....27938412.....502139307....8505203924
%C .16..4863...405404...21792634....910553970...31597696508.1003858789731
%C .16.11684..1922824..202647943..16647316316.1127672103190
%C .32.47994.15957927.3370994234.551914186148
%H R. H. Hardin, <a href="/A240394/b240394.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-2)
%F k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
%F k=3: [order 48] for n>49
%F Empirical for row n:
%F n=1: a(n) = 1
%F n=2: a(n) = 2*n + 1 for n>1
%F n=3: a(n) = (1/6)*n^4 - (5/6)*n^3 + (13/3)*n^2 + (31/3)*n - 48 for n>5
%F n=4: [polynomial of degree 14] for n>13
%F n=5: [polynomial of degree 44] for n>38
%e Some solutions for n=4 k=4
%e ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
%e ..1..0..3..3....1..0..0..3....1..3..3..0....1..0..0..0....3..2..0..0
%e ..3..0..2..2....3..0..2..3....3..1..3..2....3..0..2..0....1..2..2..3
%e ..3..0..1..1....1..3..2..0....1..2..2..2....3..0..2..0....3..2..2..2
%Y Column 1 is A016116
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Apr 04 2014
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