A181851 - OEIS

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

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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