A240338 T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4

2, 4, 4, 7, 15, 7, 11, 48, 48, 11, 16, 125, 316, 125, 16, 22, 284, 1543, 1543, 284, 22, 29, 582, 6271, 14456, 6271, 582, 29, 37, 1097, 22116, 110327, 110327, 22116, 1097, 37, 46, 1932, 69596, 716770, 1607848, 716770, 69596, 1932, 46, 56, 3219, 199504, 4106515

Offset

1,1

Comments

Table starts

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

..4...15......48.......125..........284...........582...........1097

..7...48.....316......1543.........6271.........22116..........69596

.11..125....1543.....14456.......110327........716770........4106515

.16..284....6271....110327......1607848......19629542......208224462

.22..582...22116....716770.....19629542.....455506837.....9073358239

.29.1097...69596...4106515....208224462....9073358239...342013040533

.37.1932..199504..21225132...1979743527..160455447637.11361329151015

.46.3219..528924.100450928..17168302936.2579449716281

.56.5123.1310622.439636230.137234695613

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: [polynomial of degree 5] for n>2

k=3: [polynomial of degree 13] for n>12

k=4: [polynomial of degree 30] for n>35

k=5: [polynomial of degree 69] for n>88

Example

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

Crossrefs

Column 1 is A000124

Sequence in context: A268995 A205744 A237859 * A227103 A223644 A223637

Adjacent sequences: A240335 A240336 A240337 * A240339 A240340 A240341

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved