A240394 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

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, 493, 8, 1, 15, 206, 3064, 8656, 10291, 1184, 16, 1, 17, 351, 9075, 50756, 142016, 48826, 4863, 16, 1, 19, 568, 27120, 263816, 1568581, 1314136, 405404, 11684, 32, 1, 21, 882

Offset

1,3

Comments

Table starts

..1.....1........1..........1............1.............1.............1

..2.....5........7..........9...........11............13............15

..2....12.......32.........62..........118...........206...........351

..4....50......258........954.........3064..........9075.........27120

..4...120.....1232.......8656........50756........263816.......1378418

..8...493....10291.....142016......1568581......14958462.....138422394

..8..1184....48826....1314136.....27938412.....502139307....8505203924

.16..4863...405404...21792634....910553970...31597696508.1003858789731

.16.11684..1922824..202647943..16647316316.1127672103190

.32.47994.15957927.3370994234.551914186148

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)

k=3: [order 48] for n>49

Empirical for row n:

n=1: a(n) = 1

n=2: a(n) = 2*n + 1 for n>1

n=3: a(n) = (1/6)*n^4 - (5/6)*n^3 + (13/3)*n^2 + (31/3)*n - 48 for n>5

n=4: [polynomial of degree 14] for n>13

n=5: [polynomial of degree 44] for n>38

Example

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

Crossrefs

Column 1 is A016116

Sequence in context: A134566 A128694 A088421 * A259447 A228823 A249756

Adjacent sequences: A240391 A240392 A240393 * A240395 A240396 A240397

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved