A181845 - OEIS

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A181845

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.

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

1,3

COMMENTS

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.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

EXAMPLE

[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

MAPLE

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:

PROG

(PARI) Row(n)={my(v=vector(n)); forpart(p=n, my(i=#p); v[i]=max(v[i], lcm(Vec(p)))); Vecrev(v)}

{ for(n=1, 10, print(Row(n))) } \\ Andrew Howroyd, Apr 20 2021

CROSSREFS

Cf. A181842, A181843, A181844.

Sequence in context: A119585 A195097 A329288 * A183534 A066040 A318806

Adjacent sequences: A181842 A181843 A181844 * A181846 A181847 A181848

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 07 2010

EXTENSIONS

Terms a(56) and beyond from Andrew Howroyd, Apr 20 2021

STATUS

approved