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.

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

Author

R. H. Hardin, Apr 04 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..97

Crossrefs

Column 1 is A078040

Row 1 is A016116(n+1)

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