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%I #8 May 13 2017 16:50:14
%S 1,3,1,6,4,1,10,11,4,1,15,25,12,4,1,21,51,31,12,4,1,28,97,73,32,12,4,
%T 1,36,176,162,79,32,12,4,1,45,309,345,185,80,32,12,4,1,55,530,713,418,
%U 191,80,32,12,4,1,66,894,1441,920,441,192,80,32,12,4,1
%N Triangular array T: T(n,k) = number of subset S of {1,2,...,n+1} such that |S| > 1 and max(S*) = k, where S* is the set {x(2)-x(1), x(3)-x(2), ..., x(h+1)-x(h)} when the elements of S are written as x(1) < x(2) < ... < x(h+1).
%C Column 1: A000217. Conjectures: Column 2 = A014162, and the rows have a limiting tail (1,4,12,32,...) = A001787.
%e First nine rows:
%e 1
%e 3 1
%e 6 4 1
%e 10 11 4 1
%e 15 25 12 4 1
%e 21 51 31 12 4 1
%e 28 97 73 32 12 4 1
%e 36 172 162 79 32 12 4 1
%e 45 309 345 185 80 32 12 4 1
%e T(3,1) counts these 6 subsets: {1,2}, {2,3}, {3,4}, {1,2,3}, {2,3,4}, {1,2,3,4};
%e T(3,2) counts these 4 subsets: {1,3}, {2,4}, {1,2,4}, {1,3,4};
%e T(3,3) = counts this subset: {1,4}.
%t s[n_] := Subsets[Range[1, n]]; v[n_] := Map[Max, Map[Differences, s[n]]]
%t t = Table[Count[v[n], k], {n, 1, 15}, {k, 1, n - 1}]
%t Flatten[t] (* A255874 sequence *)
%t TableForm[t] (* A255874 array *)
%Y Cf. A000217, A014162.
%K nonn,tabl,easy
%O 1,2
%A _Clark Kimberling_, Mar 08 2015
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