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

Author

R. H. Hardin, Mar 09 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A016116

Row 2 is A000027(n+1)

Row 3 is A000124

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