A239030 T(n,k)=Number of nXk 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3

1, 1, 2, 1, 3, 2, 1, 4, 4, 4, 1, 5, 7, 11, 4, 1, 6, 11, 28, 16, 8, 1, 7, 16, 59, 54, 43, 8, 1, 8, 22, 110, 149, 212, 64, 16, 1, 9, 29, 189, 354, 806, 428, 171, 16, 1, 10, 37, 306, 757, 2592, 2195, 1652, 256, 32, 1, 11, 46, 473, 1495, 7265, 9319, 11768, 3410, 683, 32, 1, 12, 56

Offset

1,3

Comments

Table starts

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

..2...3.....4......5.......6........7.........8.........9.........10

..2...4.....7.....11......16.......22........29........37.........46

..4..11....28.....59.....110......189.......306.......473........704

..4..16....54....149.....354......757......1495......2773.......4888

..8..43...212....806....2592.....7265.....18362.....42809......93464

..8..64...428...2195....9319....33699....107611....311585.....833304

.16.171..1652..11768...69288...339315...1435014...5388959...18371174

.16.256..3410..33417..265247..1719471...9453266..45358859..194626082

.32.683.13004.177087.1965398.17562449.131139508.838702960.4711005062

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-2) -4*a(n-4)

k=3: a(n) = 17*a(n-2) -96*a(n-4) +210*a(n-6) -152*a(n-8)

k=4: [order 18]

k=5: [order 38]

k=6: [order 90]

Empirical for row n:

n=1: a(n) = 1

n=2: a(n) = n + 1

n=3: a(n) = (1/2)*n^2 + (1/2)*n + 1

n=4: a(n) = (1/12)*n^4 - (1/6)*n^3 + (47/12)*n^2 - (29/6)*n + 5

n=5: [polynomial of degree 6] for n>1

n=6: [polynomial of degree 9] for n>2

n=7: [polynomial of degree 12] for n>3

Example

Some solutions for n=5 k=4
..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
..2..0..0..0....1..2..2..0....2..0..0..0....1..0..2..2....1..2..2..0
..1..0..2..2....2..1..2..0....1..0..2..2....2..0..1..2....2..1..2..0
..2..0..1..1....2..0..1..2....1..0..2..1....2..0..0..1....2..0..1..2
..1..0..2..2....1..0..2..2....2..0..0..0....1..0..2..1....1..2..2..1

Crossrefs

Column 1 is A016116

Row 2 is A000027(n+1)

Row 3 is A000124

Sequence in context: A366986 A209562 A259344 * A165999 A049280 A108786

Adjacent sequences: A239027 A239028 A239029 * A239031 A239032 A239033

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 09 2014

Status

approved