A223062 - OEIS

A223062

T(n,k)=Number of nXk 0..3 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..3 introduced in row major order

1, 2, 2, 5, 10, 5, 15, 114, 114, 15, 51, 1473, 4865, 1473, 51, 187, 19360, 213469, 213469, 19360, 187, 715, 255045, 9383963, 31331820, 9383963, 255045, 715, 2795, 3361024, 412602889, 4606719559, 4606719559, 412602889, 3361024, 2795, 11051, 44294253

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Table starts

...1......2.........5...........15...............51.................187

...2.....10.......114.........1473............19360..............255045

...5....114......4865.......213469..........9383963...........412602889

..15...1473....213469.....31331820.......4606719559........677531592132

..51..19360...9383963...4606719559....2266567594841....1115636153544055

.187.255045.412602889.677531592132.1115636153544055.1837966217755803448

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..127

FORMULA

Empirical for column k:

k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

k=2: a(n) = 18*a(n-1) -71*a(n-2) +102*a(n-3) -48*a(n-4) for n>5

k=3: a(n) = 55*a(n-1) -515*a(n-2) +1337*a(n-3) -696*a(n-4) -1188*a(n-5) +1008*a(n-6) for n>7

k=4: [order 11 for n>12]

EXAMPLE

Some solutions for n=3 k=4

..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..1....0..1..1..0

..2..2..0..1....2..1..0..2....2..3..0..2....2..1..2..2....0..2..3..0

..3..3..3..3....2..3..1..0....2..1..2..0....3..2..3..0....0..2..0..1

CROSSREFS

Column 1 is A007581(n-1)

Sequence in context: A208567 A273968 A273964 * A208788 A246864 A262924

Adjacent sequences: A223059 A223060 A223061 * A223063 A223064 A223065

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 13 2013

STATUS

approved