A368557 Number of compositions of n such that the set of absolute differences is a subset of the set of parts.

1, 1, 1, 3, 2, 2, 11, 10, 13, 27, 58, 87, 157, 253, 438, 850, 1462, 2474, 4472, 7716, 13544, 24115, 42360, 74013, 131038, 229009, 401946, 707293, 1242059, 2177682, 3828831, 6716062, 11777179, 20678592, 36267148, 63586772, 111556751, 195610763, 342949281

Offset

0,4

Links

Table of n, a(n) for n=0..38.

John Tyler Rascoe, Python program

Example

For n=12, composition [2,1,2,4,3] of 12 has the set of absolute differences {1,2}, which is a subset of the set of parts {1,2,3,4}, so it counts towards a(12) = 157.
a(3) = 3 compositions: [3], [2,1], [1,2].
a(6) = 11 compositions: [6], [4,2], [2,4], [3,2,1], [3,1,2], [2,3,1], [2,1,3], [1,3,2], [1,2,3], [2,1,2,1], [1,2,1,2].

Mathematica

g[0] = {{}}; g[n_Integer] := g[n] = Flatten[ParallelTable[Append[#, i] & /@ g[n - i], {i, 1, n}], 1];
isC[p_List] := Module[{d}, d = Abs[Differences[p]]; Union[d] === Union[Select[d, MemberQ[p, #] &]]];
a[n_Integer] := a[n] = Count[g[n], p_ /; isC[p]];
Monitor[Table[a[n], {n, 0, 19}], {n, Table[a[m], {m, 0, n - 1}]}] (* Robert P. P. McKone, Jan 02 2024 *)

Crossrefs

Cf. A003242, A032020, A173258, A214248, A214270.

Sequence in context: A119954 A100804 A143175 * A074248 A266004 A206703

Adjacent sequences: A368554 A368555 A368556 * A368558 A368559 A368560

Keyword

nonn

Author

John Tyler Rascoe, Dec 29 2023

Extensions

a(24)-a(38) from Alois P. Heinz, Dec 30 2023

Status

approved