A217883 T(n,k) = number of n-element 0..2 arrays with each element the minimum of k adjacent elements of a random 0..2 array of n+k-1 elements.

3, 3, 9, 3, 9, 27, 3, 9, 22, 81, 3, 9, 22, 51, 243, 3, 9, 22, 46, 121, 729, 3, 9, 22, 46, 91, 292, 2187, 3, 9, 22, 46, 86, 183, 704, 6561, 3, 9, 22, 46, 86, 153, 383, 1691, 19683, 3, 9, 22, 46, 86, 148, 274, 819, 4059, 59049, 3, 9, 22, 46, 86, 148, 244, 511, 1749, 9749, 177147

Offset

1,1

Comments

See A228461 and A217954 for more information about the definition. - N. J. A. Sloane, Sep 02 2013

Table starts

........3......3......3.....3.....3.....3....3....3....3....3....3....3....3

........9......9......9.....9.....9.....9....9....9....9....9....9....9....9

.......27.....22.....22....22....22....22...22...22...22...22...22...22...22

.......81.....51.....46....46....46....46...46...46...46...46...46...46...46

......243....121.....91....86....86....86...86...86...86...86...86...86...86

......729....292....183...153...148...148..148..148..148..148..148..148..148

.....2187....704....383...274...244...239..239..239..239..239..239..239..239

.....6561...1691....819...511...402...372..367..367..367..367..367..367..367

....19683...4059...1749...993...685...576..546..541..541..541..541..541..541

....59049...9749...3699..1966..1223...915..806..776..771..771..771..771..771

...177147..23422...7772..3880..2263..1520.1212.1103.1073.1068.1068.1068.1068

...531441..56268..16316..7558..4243..2639.1896.1588.1479.1449.1444.1444.1444

..1594323.135166..34325.14544..7910..4711.3107.2364.2056.1947.1917.1912.1912

..4782969.324692..72349.27819.14528..8471.5285.3681.2938.2630.2521.2491.2486

.14348907.779977.152573.53226.26274.15107.9166.5980.4376.3633.3325.3216.3186

Links

R. H. Hardin, Table of n, a(n) for n = 1..902

Formula

Empirical for column k:

k=2: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)

k=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-4) -a(n-5) +a(n-6) +a(n-7)

k=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-5) -a(n-6) +a(n-7) +a(n-8) +a(n-9)

k=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-6) -a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11)

k=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-7) -a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13)

k=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +3*a(n-8) -a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15)

Diagonal: a(n) = (1/24)*n^4 + (1/4)*n^3 + (23/24)*n^2 + (3/4)*n + 1

Example

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

Crossrefs

Column 2 is A202882(n+1). Cf. A228461, A217954, A217878.

Sequence in context: A160121 A048883 A241717 * A036553 A339318 A359600

Adjacent sequences: A217880 A217881 A217882 * A217884 A217885 A217886

Keyword

nonn,tabl

Author

R. H. Hardin, observation that the diagonal is a polynomial from L. Edson Jeffery in the Sequence Fans Mailing List, Oct 14 2012

Status

approved