# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a240675
Showing 1-1 of 1

%I A240675 #12 Jun 05 2015 08:28:37
%S A240675 1,0,0,3,4,6,8,8,9,22,22,34,50,60,74,105,120,144,186,234,280,358,440,
%T A240675 524,665,782,954,1150,1354,1630,1944,2258,2666,3170,3728,4365,5128,
%U A240675 5976,6978,8144,9488,10952,12700,14716,16932,19558,22434,25764,29505,33782
%N A240675 Number of partitions p of n such that exactly one number is in both p and its conjugate.
%C A240675 Second column of the array at A240181.  Multiplicities greater than 1 are not counted; e.g. there is exactly one number that is in both {4,1,1} and {3,1,1,1}.
%H A240675 Manfred Scheucher, <a href="/A240675/b240675.txt">Table of n, a(n) for n = 1..65</a>
%H A240675 Manfred Scheucher, <a href="/A240675/a240675.sage.txt">Sage Script</a>
%e A240675 a(6) counts these 6 partitions:  51, 42, 411, 3111, 2211, 21111, of which the respective conjugates are 21111, 2211, 3111, 411, 42, 51.
%t A240675 z = 30; p[n_, k_] := p[n, k] = IntegerPartitions[n][[k]]; c[p_] := c[p] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; b[n_] := b[n] = Table[Intersection[p[n, k], c[p[n, k]]], {k, 1, PartitionsP[n]}]; Table[Count[Map[Length, b[n]], 0], {n, 1, z}] (* A240674 *)
%t A240675 Table[Count[Map[Length, b[n]], 1], {n, 1, z}]   (* A240675 *)
%o A240675 (PARI) conjug(v) = {my(m = matrix(#v, vecmax(v))); for (i=1, #v, for (j=1, v[i], m[i, j] = 1;);); vector(vecmax(v), i, sum(j=1, #v, m[j, i]));}
%o A240675 a(n) = {my(v = partitions(n)); my(nb = 0); for (k=1, #v, if (#setintersect(Set(v[k]), Set(conjug(v[k]))) == 1, nb++);); nb;} \\ _Michel Marcus_, Jun 02 2015
%Y A240675 Cf. A240674, A240181.
%K A240675 nonn,easy
%O A240675 1,4
%A A240675 _Clark Kimberling_, Apr 12 2014
%E A240675 More terms from _Manfred Scheucher_, Jun 01 2015

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE