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%I #10 May 31 2018 06:05:47
%S 1,0,3,3,3,7,9,12,14,22,30,39,41,57,86,87,121,179,164,225,300,362,433,
%T 571,624,846,968,1134,1391,1902,1992,2407,3043,3688,4321,5145,5811,
%U 7277,8627,10234
%N Number of conjugate-congruent partitions of n.
%C See reference for precise definition.
%C Let P be a partition of n and let Q denote its conjugate partition. Then P is said to be conjugate-congruent if there is an integer m>1 such that both P and Q give the same set R(P,m) of residues when their parts are reduced modulo m, where R(P,m) contains less than m elements. - _Augustine O. Munagi_, Dec 18 2008
%H A. O. Munagi, <a href="http://dx.doi.org/10.1016/j.disc.2007.05.022">Pairing conjugate partitions by residue classes</a>, Discrete Math., 308 (2008), 2492-2501.
%e a(8) = 12: the 12 conjugate-congruent partitions of 8 are shown below, in conjugate pairs followed by their common residues. 8/1+1+1+1+1+1+1+1 by 1 mod 7, 1+7/1+1+1+1+1+1+2 by 1,2 mod 5, 2+6/1+1+1+1+2+2 by 1,2 mod 5, 4+4/2+2+2+2 by 0 mod 2, 1+1+6/1+1+1+1+1+3 by 0,1 mod 3, 2+3+3/2+3+3 by 0,2 mod 3, 1+1+2+4/1+1+2+4 by 1,2 mod 3. - _Augustine O. Munagi_, Dec 18 2008
%p with(combinat): isconjcong:=proc(P::partition) local m; option remember; if P[ -1]>=conjpart(P)[ -1] then for m from 2 to P[ -1]+1 do if {op(P mod m)}={op(conjpart(P) mod m)} and nops({op(P mod m)})<m then return true; end if; end do; else for m from 2 to conjpart(P)[ -1]+1 do if {op(P mod m)}={op(conjpart(P) mod m)} and nops({op(P mod m)})<m then return true; end if; end do; end if; false; end proc: seq(nops(select(isconjcong,partition(n))),n=1..30); # _Augustine O. Munagi_, Dec 18 2008
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_ May 07 2008
%E a(36)-a(40) from _Augustine O. Munagi_, Dec 18 2008
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