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A229012 T(n,k) = number of arrays of median of three adjacent elements of some length n+2 0..k array, with no adjacent equal elements in the latter.

%I A229012 #8 Sep 13 2013 20:10:12
%S A229012 2,3,2,4,7,2,5,14,15,2,6,23,46,31,2,7,34,101,130,57,2,8,47,186,359,
%T A229012 332,105,2,9,62,307,794,1145,830,193,2,10,79,470,1527,3002,3527,2054,
%U A229012 353,2,11,98,681,2666,6635,10860,10735,5108,653,2,12,119,946,4335,13040,27379
%N A229012 T(n,k) = number of arrays of median of three adjacent elements of some length n+2 0..k array, with no adjacent equal elements in the latter.
%C A229012 Table starts
%C A229012 .2...3.....4......5......6.......7.......8........9.......10.......11........12
%C A229012 .2...7....14.....23.....34......47......62.......79.......98......119.......142
%C A229012 .2..15....46....101....186.....307.....470......681......946.....1271......1662
%C A229012 .2..31...130....359....794....1527....2666.....4335.....6674.....9839.....14002
%C A229012 .2..57...332...1145...3002....6635...13040....23515....39698....63605.....97668
%C A229012 .2.105...830...3527..10860...27379...60180...119653...220318...381749....629586
%C A229012 .2.193..2054..10735..38768..111311..273124...597477..1197190..2238005...3954490
%C A229012 .2.353..5108..32907.139456..456029.1248872..3004839..6549040.13200731..24974126
%C A229012 .2.653.12790.101635.506236.1888383.5780144.15315095.36345246.79063593.160271154
%H A229012 R. H. Hardin, <a href="/A229012/b229012.txt">Table of n, a(n) for n = 1..925</a>
%F A229012 Empirical for column k:
%F A229012 k=1: a(n) = a(n-1)
%F A229012 k=2: [order 13]
%F A229012 k=3: [order 27]
%F A229012 k=4: [order 46]
%F A229012 k=5: [order 69]
%F A229012 k=6: [order 95] for n>97
%F A229012 Empirical for row n:
%F A229012 n=1: a(n) = 1*n + 1
%F A229012 n=2: a(n) = 1*n^2 + 2*n - 1
%F A229012 n=3: a(n) = 1*n^3 + 3*n^2 - 3*n + 1
%F A229012 n=4: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1
%F A229012 n=5: [polynomial of degree 5]
%F A229012 n=6: [polynomial of degree 6]
%F A229012 n=7: [polynomial of degree 7]
%e A229012 Some solutions for n=4 k=4
%e A229012 ..1....1....0....3....4....1....2....3....2....3....3....1....1....0....2....2
%e A229012 ..4....1....1....1....3....0....2....1....0....0....2....3....4....4....0....1
%e A229012 ..0....1....3....3....3....2....0....1....4....2....2....4....1....1....3....3
%e A229012 ..3....2....3....1....0....0....1....3....3....1....0....3....4....4....2....3
%Y A229012 Row 2 is A008865(n+1).
%K A229012 nonn,tabl
%O A229012 1,1
%A A229012 _R. H. Hardin_, Sep 10 2013