

A238812


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


8



2, 3, 3, 4, 8, 4, 5, 15, 15, 5, 6, 25, 48, 25, 6, 7, 39, 118, 118, 39, 7, 8, 58, 254, 468, 254, 58, 8, 9, 83, 498, 1501, 1501, 498, 83, 9, 10, 115, 916, 4167, 7502, 4167, 916, 115, 10, 11, 155, 1605, 10423, 31125, 31125, 10423, 1605, 155, 11, 12, 204, 2702, 24115
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OFFSET

1,1


COMMENTS

Table starts
..2...3....4......5.......6........7..........8...........9...........10
..3...8...15.....25......39.......58.........83.........115..........155
..4..15...48....118.....254......498........916........1605.........2702
..5..25..118....468....1501.....4167......10423.......24115........52449
..6..39..254...1501....7502....31125.....111564......356666......1041746
..7..58..498...4167...31125...197418....1055763.....4880856.....19977948
..8..83..916..10423..111564..1055763....8526852....58670336....348923836
..9.115.1605..24115..356666..4880856...58670336...605163204...5342432459
.10.155.2702..52449.1041746.19977948..348923836..5342432459..70386525080
.11.204.4395.108395.2828429.73988808.1828642499.40798150971.796431939717


LINKS



FORMULA

k=1: a(n) = n + 1
k=2: a(n) = (1/6)*n^3 + (23/6)*n  1
k=3: [polynomial of degree 6] for n>2
k=4: [polynomial of degree 10] for n>4
k=5: [polynomial of degree 15] for n>6
k=6: [polynomial of degree 21] for n>8
k=7: [polynomial of degree 28] for n>10


EXAMPLE

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


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



