login
A240381
T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4
10
2, 2, 4, 4, 10, 10, 4, 38, 44, 22, 8, 90, 330, 148, 50, 8, 366, 1494, 2066, 636, 114, 16, 878, 12234, 17550, 16994, 2430, 258, 16, 3606, 57722, 279886, 281186, 116030, 9648, 586, 32, 8666, 477574, 2545618, 8802558, 3502886, 884792, 37946, 1330, 32, 35602
OFFSET
1,1
COMMENTS
Table starts
....2......2.........4............4.............8..............8.............16
....4.....10........38...........90...........366............878...........3606
...10.....44.......330.........1494.........12234..........57722.........477574
...22....148......2066........17550........279886........2545618.......41758418
...50....636.....16994.......281186.......8802558......157432290.....5145703760
..114...2430....116030......3502886.....207932244.....7149227810...457988195982
..258...9648....884792.....52375114....6169009514...422227556156.54164128056204
..586..37946...6273952....672652728..148090588518.19320096061230
.1330.149336..46648918...9771038498.4275011910288
.3018.588102.335571098.127878632630
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
k=2: [order 14] for n>15
Empirical for row n:
n=1: a(n) = 2*a(n-2)
n=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
n=3: [order 48] for n>50
EXAMPLE
Some solutions for n=4 k=4
..1..3..1..3....3..1..1..3....3..1..3..1....3..1..3..1....1..3..1..3
..1..3..1..3....3..0..2..0....3..1..2..1....3..0..2..0....1..2..2..2
..1..2..1..1....3..2..0..2....3..2..2..2....1..0..0..0....1..2..0..0
..3..0..0..2....2..0..0..0....1..0..0..0....2..0..1..2....2..3..2..1
CROSSREFS
Column 1 is A078040
Row 1 is A016116(n+1)
Sequence in context: A114338 A170831 A133406 * A295746 A272104 A285436
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 04 2014
STATUS
approved