cp's OEIS Frontend

A255874 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).

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