login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322439 Number of ordered pairs of integer partitions of n where no part of the first is greater than any part of the second. 7

%I

%S 1,1,3,5,11,15,33,42,82,114,195,258,466,587,954,1317,2021,2637,4124,

%T 5298,7995,10565,15075,19665,28798,36773,51509,67501,93060,119299,

%U 165589,209967,285535,366488,487536,622509,833998,1048119,1380410,1754520,2291406,2876454

%N Number of ordered pairs of integer partitions of n where no part of the first is greater than any part of the second.

%H Alois P. Heinz, <a href="/A322439/b322439.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k = 1...n} A026820(n, k) * A026794(n, k).

%e The a(5) = 15 pairs of integer partitions:

%e (5)|(5)

%e (41)|(5)

%e (32)|(5)

%e (311)|(5)

%e (221)|(5)

%e (221)|(32)

%e (2111)|(5)

%e (2111)|(32)

%e (11111)|(5)

%e (11111)|(41)

%e (11111)|(32)

%e (11111)|(311)

%e (11111)|(221)

%e (11111)|(2111)

%e (11111)|(11111)

%p g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

%p g(n, i-1) +g(n-i, min(i, n-i)))

%p end:

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p `if`(i>n, 0, b(n, i+1)+b(n-i, i)))

%p end:

%p a:= proc(n) option remember; `if`(n=0, 1,

%p add(g(n, i)*b(n-i, i), i=1..n))

%p end:

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Dec 09 2018

%t Table[Length[Select[Tuples[IntegerPartitions[n],2],Max@@First[#]<=Min@@Last[#]&]],{n,20}]

%Y Cf. A026794, A026820, A265947, A285573, A317144, A318915, A322435, A322436, A322440, A322441, A322442.

%K nonn

%O 0,3

%A _Gus Wiseman_, Dec 08 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 7 16:08 EDT 2020. Contains 335496 sequences. (Running on oeis4.)