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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.

%I A217883 #8 Sep 02 2013 09:54:11
%S A217883 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 A217883 292,2187,3,9,22,46,86,183,704,6561,3,9,22,46,86,153,383,1691,19683,3,
%U A217883 9,22,46,86,148,274,819,4059,59049,3,9,22,46,86,148,244,511,1749,9749,177147
%N 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.
%C A217883 See A228461 and A217954 for more information about the definition. - _N. J. A. Sloane_, Sep 02 2013
%C A217883 Table starts
%C A217883 ........3......3......3.....3.....3.....3....3....3....3....3....3....3....3
%C A217883 ........9......9......9.....9.....9.....9....9....9....9....9....9....9....9
%C A217883 .......27.....22.....22....22....22....22...22...22...22...22...22...22...22
%C A217883 .......81.....51.....46....46....46....46...46...46...46...46...46...46...46
%C A217883 ......243....121.....91....86....86....86...86...86...86...86...86...86...86
%C A217883 ......729....292....183...153...148...148..148..148..148..148..148..148..148
%C A217883 .....2187....704....383...274...244...239..239..239..239..239..239..239..239
%C A217883 .....6561...1691....819...511...402...372..367..367..367..367..367..367..367
%C A217883 ....19683...4059...1749...993...685...576..546..541..541..541..541..541..541
%C A217883 ....59049...9749...3699..1966..1223...915..806..776..771..771..771..771..771
%C A217883 ...177147..23422...7772..3880..2263..1520.1212.1103.1073.1068.1068.1068.1068
%C A217883 ...531441..56268..16316..7558..4243..2639.1896.1588.1479.1449.1444.1444.1444
%C A217883 ..1594323.135166..34325.14544..7910..4711.3107.2364.2056.1947.1917.1912.1912
%C A217883 ..4782969.324692..72349.27819.14528..8471.5285.3681.2938.2630.2521.2491.2486
%C A217883 .14348907.779977.152573.53226.26274.15107.9166.5980.4376.3633.3325.3216.3186
%H A217883 R. H. Hardin, <a href="/A217883/b217883.txt">Table of n, a(n) for n = 1..902</a>
%F A217883 Empirical for column k:
%F A217883 k=2: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)
%F A217883 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 A217883 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 A217883 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 A217883 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 A217883 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 A217883 Diagonal: a(n) = (1/24)*n^4 + (1/4)*n^3 + (23/24)*n^2 + (3/4)*n + 1
%e A217883 Some solutions for n=4 k=4
%e A217883 ..0....0....2....1....0....0....1....2....0....2....2....1....0....2....1....1
%e A217883 ..2....2....2....1....0....0....1....1....1....2....1....2....2....2....1....2
%e A217883 ..1....2....2....1....0....2....2....0....2....2....1....2....2....2....2....2
%e A217883 ..0....0....0....1....1....0....1....0....0....2....1....1....2....1....0....2
%Y A217883 Column 2 is A202882(n+1). Cf. A228461, A217954, A217878.
%K A217883 nonn,tabl
%O A217883 1,1
%A A217883 _R. H. Hardin_, observation that the diagonal is a polynomial from _L. Edson Jeffery_ in the Sequence Fans Mailing List, Oct 14 2012