A217883 - OEIS

%I #8 Sep 02 2013 09:54:11

%S 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,

%T 292,2187,3,9,22,46,86,183,704,6561,3,9,22,46,86,153,383,1691,19683,3,

%U 9,22,46,86,148,274,819,4059,59049,3,9,22,46,86,148,244,511,1749,9749,177147

%N 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.

%C See A228461 and A217954 for more information about the definition. - _N. J. A. Sloane_, Sep 02 2013

%C Table starts

%C ........3......3......3.....3.....3.....3....3....3....3....3....3....3....3

%C ........9......9......9.....9.....9.....9....9....9....9....9....9....9....9

%C .......27.....22.....22....22....22....22...22...22...22...22...22...22...22

%C .......81.....51.....46....46....46....46...46...46...46...46...46...46...46

%C ......243....121.....91....86....86....86...86...86...86...86...86...86...86

%C ......729....292....183...153...148...148..148..148..148..148..148..148..148

%C .....2187....704....383...274...244...239..239..239..239..239..239..239..239

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

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

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

%C ...177147..23422...7772..3880..2263..1520.1212.1103.1073.1068.1068.1068.1068

%C ...531441..56268..16316..7558..4243..2639.1896.1588.1479.1449.1444.1444.1444

%C ..1594323.135166..34325.14544..7910..4711.3107.2364.2056.1947.1917.1912.1912

%C ..4782969.324692..72349.27819.14528..8471.5285.3681.2938.2630.2521.2491.2486

%C .14348907.779977.152573.53226.26274.15107.9166.5980.4376.3633.3325.3216.3186

%H R. H. Hardin, <a href="/A217883/b217883.txt">Table of n, a(n) for n = 1..902</a>

%F Empirical for column k:

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

%F 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)

%F 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)

%F 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)

%F 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)

%F 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)

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

%e Some solutions for n=4 k=4

%e ..0....0....2....1....0....0....1....2....0....2....2....1....0....2....1....1

%e ..2....2....2....1....0....0....1....1....1....2....1....2....2....2....1....2

%e ..1....2....2....1....0....2....2....0....2....2....1....2....2....2....2....2

%e ..0....0....0....1....1....0....1....0....0....2....1....1....2....1....0....2

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, observation that the diagonal is a polynomial from _L. Edson Jeffery_ in the Sequence Fans Mailing List, Oct 14 2012