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A181842 Triangle read by rows: T(n,k) = Sum_{c in partition(n,n-k+1)} lcm(c) 8
1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 5, 10, 5, 1, 2, 5, 12, 12, 6, 1, 2, 5, 12, 18, 28, 7, 1, 2, 5, 12, 20, 38, 32, 8, 1, 2, 5, 12, 20, 44, 57, 48, 9, 1, 2, 5, 12, 20, 46, 67, 100, 55, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
In A181842 through A181854 the following terminology is used.
Let n, k be positive integers.
* Partition: A (n,k)-partition is the set of all k-sets of
positive integers whose elements sum to n.
- The cardinality of a (n,k)-partition: A008284(n,k).
- Maple: (n,k) -> combstruct[count](Partition(n),size=k).
- The (6,2)-partition is {{1,5},{2,4},{3,3}}.
* Composition: A (n,k)-composition is the set of all k-tuples of positive integers whose elements sum to n.
- The cardinality of a (n,k)-composition: A007318(n-1,k-1).
- Maple: (n,k) -> combstruct[count](Composition(n),size=k).
- The (6,2)-composition is {<5,1>,<4,2>,<3,3>,<2,4>,<1,5>}.
* Combination: A (n,k)-combination is the set of all k-subsets
of {1,2,..,n}.
- The cardinality of a (n,k)-combination: A007318(n,k).
- Maple: (n,k) -> combstruct[count](Combination(n),size=k).
- The (4,2)-combination is {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}.
LINKS
EXAMPLE
[1] 1
[2] 1 2
[3] 1 2 3
[4] 1 2 5 4
[5] 1 2 5 10 5
[6] 1 2 5 12 12 6
[7] 1 2 5 12 18 28 7
MAPLE
with(combstruct):
a181842_row := proc(n) local k, L, l, R, part;
R := NULL;
for k from 1 to n do
L := 0;
part := iterstructs(Partition(n), size=n-k+1):
while not finished(part) do
l := nextstruct(part);
L := L + ilcm(op(l));
od;
R := R, L;
od;
R end:
MATHEMATICA
t[n_, k_] := LCM @@@ IntegerPartitions[n, {n - k + 1}] // Total; Table[t[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 26 2013 *)
CROSSREFS
Sequence in context: A064882 A065158 A364842 * A209564 A029653 A067763
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 07 2010
STATUS
approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)