login
A225751
Number of different figures obtained by a putting two Young diagrams of partitions lambda and mu, such that |lambda| + |mu| = n on top of each other.
1
1, 1, 3, 5, 10, 15, 26, 38, 60, 85, 127, 176, 253, 343, 478, 639, 870, 1145, 1530, 1990, 2617, 3367, 4369, 5568, 7143, 9024, 11460, 14369, 18087, 22517, 28121, 34787, 43136, 53048, 65358, 79944, 97921, 119173, 145188, 175883, 213221, 257177, 310351, 372820
OFFSET
0,3
COMMENTS
See Mukhin reference item 4.3. 'A challenge', sum of p(k) for k = ceiling(n/2) to n with p(k) the partition numbers A000041. Remark that the indexing in the reference misses N_3 (should be N_3=5 and so on).
FORMULA
a(n) = Sum_{i=ceiling(n/2)..n} A000041(i).
a(n) = A000070(n) - A000070(ceiling(n/2)-1). - Alois P. Heinz, Jul 31 2016
EXAMPLE
a(3) = 5 is illustrated by the following 5 different results:
{2} = {1} & {2}
{2} = {2} & {1}
{3} = { } & {3}
{1,1} = {1} & {1,1}
{1,1} = {1,1}& {1}
{2,1} = { } & {2,1}
{1,1,1}= { } & {1,1,1}
producing {2}, {3}, {1,1}, {2,1} and {1,1,1} as superpositions of two partitions with sum of lengths = 3.
MAPLE
with(combinat):
a:= n-> add(numbpart(i), i=ceil(n/2)..n):
seq(a(n), n=0..50); # Alois P. Heinz, May 15 2013
MATHEMATICA
Table[Sum[PartitionsP[k], {k, Ceiling[n/2], n}], {n, 36}]
PROG
(PARI) a(n)=sum(k=ceil(n/2), n, numbpart(k)); \\ Joerg Arndt, May 15 2013
CROSSREFS
Sequence in context: A090491 A126728 A070557 * A264397 A254346 A132302
KEYWORD
nonn
AUTHOR
Wouter Meeussen, May 14 2013
STATUS
approved