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!)
A265508 Number of unordered pairs {p,q} of partitions of n into distinct parts such that p and q are incomparable in the dominance order. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 29, 42, 68, 109, 162, 240, 364, 527, 749, 1096, 1529, 2162, 3026, 4179, 5702, 7926, 10650, 14412, 19437, 26042, 34560, 46077, 60617, 79893, 104850, 136851, 177884, 231526, 298868, 385221, 496159, 635725, 812342 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Wikipedia, Dominance Order

FORMULA

a(n) = A000217(A000009(n)) - A265506(n).

EXAMPLE

a(9) = 1: {621,54}.

a(10) = 1: {721,64}.

a(11) = 3: {821,74}, {821,65}, {731,65}.

a(12) = 5: {6321,543}, {921,84}, {921,75}, {831,75}, {732,651}.

MAPLE

b:= proc(n, m, i, j, t) option remember; `if`(n<m, 0, `if`(n=0, 1,

      `if`(i<1, 0, `if`(t and j>0, b(n, m, i, j-1, true), 0)+

      b(n, m, i-1, j, false)+b(n-i, m-j, max(0, min(n-i, i-1)),

      max(0, min(m-j, j-1)), true))))

    end:

g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

      `if`(n=0, 1, g(n, i-1)+`if`(i>n, 0, g(n-i, i-1))))

    end:

a:= n-> (t-> t*(t+1)/2)(g(n$2))-b(n$4, true):

seq(a(n), n=0..45);

MATHEMATICA

b[n_, m_, i_, j_, t_] := b[n, m, i, j, t] = If[n < m, 0, If[n == 0, 1, If[i < 1, 0, If[t && j > 0, b[n, m, i, j-1, True], 0] + b[n, m, i-1, j, False] + b[n-i, m-j, Max[0, Min[n-i, i-1]], Max[0, Min[m-j, j-1]], True]]]]; g[n_, i_] := g[n, i] = If[i*(i+1)/2 < n, 0, If[n == 0, 1, g[n, i-1] + If[i > n, 0, g[n-i, i-1]]]]; a[n_] := (#*(#+1)/2&)[g[n, n]] - b[n, n, n, n, True]; Table[a[n], {n, 0, 45}] (* Jean-Fran├žois Alcover, Feb 05 2017, translated from Maple *)

CROSSREFS

Cf. A000009, A000217, A248476, A265506.

Sequence in context: A077285 A072523 A054473 * A327042 A006168 A250115

Adjacent sequences:  A265505 A265506 A265507 * A265509 A265510 A265511

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 09 2015

STATUS

approved

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 August 12 21:10 EDT 2020. Contains 336440 sequences. (Running on oeis4.)