A181851 Triangle read by rows: T(n,k) = Sum_{c in composition(n,k)} lcm(c).

1, 2, 1, 3, 4, 1, 4, 8, 6, 1, 5, 20, 15, 8, 1, 6, 21, 50, 24, 10, 1, 7, 56, 66, 96, 35, 12, 1, 8, 60, 180, 160, 160, 48, 14, 1, 9, 96, 264, 432, 325, 244, 63, 16, 1, 10, 105, 510, 776, 892, 585, 350, 80, 18, 1, 11, 220, 567, 1704, 1835, 1668, 966, 480, 99, 20, 1

Offset

1,2

Comments

Composition(n,k) is the set of the k-tuples of positive integers which sum to n (see A181842). Taking the example in A181842, T(6,2) = lcm(5,1) + lcm(4,2) + lcm(3,3) + lcm(2,4) + lcm(1,5) = 5+4+3+4+5 = 21.

Links

Alois P. Heinz, Rows n = 1..150, flattened

Example

[1]   1
[2]   2    1
[3]   3    4    1
[4]   4    8    6    1
[5]   5   20   15    8    1
[6]   6   21   50   24   10    1
[7]   7   56   66   96   35   12   1

Maple

with(combstruct):
a181851_row := proc(n) local k, L, l, R, comp;
R := NULL;
for k from 1 to n do
   L := 0;
   comp := iterstructs(Composition(n), size=k):
   while not finished(comp) do
      l := nextstruct(comp);
      L := L + ilcm(op(l));
   od;
   R := R, L;
od;
R end:

Mathematica

c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[t[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 05 2014 *)

Crossrefs

Cf. A181849, A181850, A181853.

T(2n,n) gives A373865.

Sequence in context: A361042 A072506 A188236 * A210231 A180378 A208341

Adjacent sequences: A181848 A181849 A181850 * A181852 A181853 A181854

Keyword

nonn,tabl

Author

Peter Luschny, Dec 07 2010

Status

approved