A239649 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, modulo 4

2, 4, 4, 8, 20, 10, 16, 92, 112, 22, 32, 418, 1182, 560, 50, 64, 1898, 12246, 13476, 2874, 114, 128, 8588, 127454, 320314, 158728, 14788, 258, 256, 38888, 1320102, 7629186, 8634040, 1864886, 75540, 586, 512, 175974, 13703468, 181039448, 471203608

Offset

1,1

Comments

Table starts

....2.......4..........8............16...............32...................64

....4......20.........92...........418.............1898.................8588

...10.....112.......1182.........12246...........127454..............1320102

...22.....560......13476........320314..........7629186............181039448

...50....2874.....158728.......8634040........471203608..........25594620082

..114...14788....1864886.....232304146......29007348454........3608789598890

..258...75540...21813374....6219477628....1778793691226......506611939408296

..586..387306..255830770..167002115382..109328664988704....71303275040032094

.1330.1983686.2997975560.4480024646968.6715782662219974.10028169382114414238

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: [order 10]

k=3: [order 35]

Empirical for row n:

n=1: a(n) = 2*a(n-1)

n=2: a(n) = 3*a(n-1) +12*a(n-2) -18*a(n-3) -29*a(n-4) +19*a(n-5) +38*a(n-6) +8*a(n-7)

n=3: [order 25]

n=4: [order 91]

Example

Some solutions for n=3 k=4
..3..1..3..1....3..0..1..3....1..0..3..3....3..0..0..0....1..0..3..3
..2..1..2..0....2..1..1..2....1..0..3..3....2..0..3..0....1..3..2..0
..1..3..1..0....2..1..1..1....1..0..3..3....2..1..2..3....1..0..0..0

Crossrefs

Column 1 is A078040

Row 1 is A000079

Sequence in context: A160124 A295293 A080007 * A264190 A006967 A296229

Adjacent sequences: A239646 A239647 A239648 * A239650 A239651 A239652

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 23 2014

Status

approved