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).

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, 1, 36, 176, 162, 79, 32, 12, 4, 1, 45, 309, 345, 185, 80, 32, 12, 4, 1, 55, 530, 713, 418, 191, 80, 32, 12, 4, 1, 66, 894, 1441, 920, 441, 192, 80, 32, 12, 4, 1

Offset: 1

Author

Clark Kimberling, Mar 08 2015

Keywords

• nonn
• tabl
• easy

Comments

Column 1: A000217. Conjectures: Column 2 = A014162, and the rows have a limiting tail (1,4,12,32,...) = A001787.

Examples

			First nine rows:
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   1
36  172 162 79  32  12  4  1
45  309 345 185 80  32  12  4  1
T(3,1) counts these 6 subsets:  {1,2}, {2,3}, {3,4}, {1,2,3}, {2,3,4}, {1,2,3,4};
T(3,2) counts these 4 subsets:  {1,3}, {2,4}, {1,2,4}, {1,3,4};
T(3,3) = counts this subset: {1,4}.
		

Crossrefs

Cf. A000217, A014162.

Programs

Mathematica

s[n_] := Subsets[Range[1, n]]; v[n_] := Map[Max, Map[Differences, s[n]]]
t = Table[Count[v[n], k], {n, 1, 15}, {k, 1, n - 1}]
Flatten[t]   (* A255874 sequence *)
TableForm[t] (* A255874 array *)