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A228740 T(n,k) = number of arrays of the median of three adjacent elements of some length n+2 0..k array.

%I A228740 #15 Sep 02 2013 12:45:42
%S A228740 2,3,4,4,9,8,5,16,27,16,6,25,64,77,28,7,36,125,232,185,50,8,49,216,
%T A228740 545,696,447,88,9,64,343,1096,1943,2072,1071,156,10,81,512,1981,4504,
%U A228740 6797,6130,2593,278,11,100,729,3312,9191,17986,23627,18378,6333,496,12,121
%N A228740 T(n,k) = number of arrays of the median of three adjacent elements of some length n+2 0..k array.
%C A228740 See A228461 for more information about the definition. - _N. J. A. Sloane_, Sep 02 2013
%C A228740 Table starts
%C A228740 ...2....3.....4......5.......6.......7........8........9.......10........11
%C A228740 ...4....9....16.....25......36......49.......64.......81......100.......121
%C A228740 ...8...27....64....125.....216.....343......512......729.....1000......1331
%C A228740 ..16...77...232....545....1096....1981.....3312.....5217.....7840.....11341
%C A228740 ..28..185...696...1943....4504....9191....17088....29589....48436.....75757
%C A228740 ..50..447..2072...6797...17986...41083....84288...159321...282274....474551
%C A228740 ..88.1071..6130..23627...71278..181885...410828...845517..1617004...2913955
%C A228740 .156.2593.18378..83391..287154..819099..2037214..4564455..9418762..18182967
%C A228740 .278.6333.55716.298239.1174282.3749921.10282648.25107493.55950398.115793733
%H A228740 R. H. Hardin, <a href="/A228740/b228740.txt">Table of n, a(n) for n = 1..811</a>
%F A228740 Empirical for column k:
%F A228740 k=1: a(n) = 2*a(n-1) -a(n-3) +a(n-5)
%F A228740 k=2: [order 14]
%F A228740 k=3: [order 26]
%F A228740 k=4: [order 43]
%F A228740 Empirical for row n:
%F A228740 n=1: a(n) = n + 1
%F A228740 n=2: a(n) = n^2 + 2*n + 1
%F A228740 n=3: a(n) = n^3 + 3*n^2 + 3*n + 1
%F A228740 n=4: a(n) = (2/3)*n^4 + 4*n^3 + (19/3)*n^2 + 4*n + 1
%F A228740 n=5: [polynomial of degree 5]
%F A228740 n=6: [polynomial of degree 6]
%F A228740 n=7: [polynomial of degree 7]
%e A228740 Some solutions for n=4 k=4
%e A228740 ..1..4..3..2..0..4..2..2..4..1..2..0..0..0..2..1
%e A228740 ..2..0..2..0..0..3..3..4..2..2..2..1..2..2..3..4
%e A228740 ..1..3..0..0..0..1..0..1..3..1..0..0..2..3..4..4
%e A228740 ..3..1..2..1..4..1..1..4..1..2..4..0..2..2..3..3
%Y A228740 Row 1 is A000027(n+1)
%Y A228740 Row 2 is A000290(n+1)
%Y A228740 Row 3 is A000578(n+1)
%Y A228740 For other rows, columns and diagonals see A228739-A228744.
%K A228740 nonn,tabl
%O A228740 1,1
%A A228740 _R. H. Hardin_ Sep 01 2013