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A181845
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Triangle read by rows: T(n,k) = max_{c in P(n,n-k+1)} lcm(c) where P(n,m) = A008284(n,m) is the number of partitions of n into m parts.
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1
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1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 6, 5, 1, 2, 3, 6, 5, 6, 1, 2, 3, 6, 6, 12, 7, 1, 2, 3, 6, 6, 12, 15, 8, 1, 2, 3, 6, 6, 12, 15, 20, 9, 1, 2, 3, 6, 6, 12, 15, 30, 21, 10, 1, 2, 3, 6, 6, 12, 15, 30, 21, 30, 11, 1, 2, 3, 6, 6, 12, 15, 30, 30, 60, 35, 12
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OFFSET
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1,3
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COMMENTS
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See A181842 for the definition of 'partition'. T(n,k) is also the triangle read by rows: T(n,k) = max_{c in C(n,n-k+1)} lcm(c) where C(n,m) is the set of all m-tuples of positive integers whose elements sum to n where the C(n,k) = A007318(n-1,k-1) are called compositions of n of size k.
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LINKS
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EXAMPLE
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[1] 1
[2] 1 2
[3] 1 2 3
[4] 1 2 3 4
[5] 1 2 3 6 5
[6] 1 2 3 6 5 6
[7] 1 2 3 6 6 12 7
[8] 1 2 3 6 6 12 15 8
[9] 1 2 3 6 6 12 15 20 9
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MAPLE
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with(combstruct):
a181845_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):
# alternatively (but slower)
# part := iterstructs(Composition(n), size=n-k+1):
while not finished(part) do
l := nextstruct(part);
L := max(L, ilcm(op(l)));
od;
R := R, L;
od;
R end:
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PROG
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(PARI) Row(n)={my(v=vector(n)); forpart(p=n, my(i=#p); v[i]=max(v[i], lcm(Vec(p)))); Vecrev(v)}
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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