cp's OEIS Frontend

A067627 Triangle T(n,k) = number of conjugacy classes of partitions of n using only k types of piles, read by rows.

%I A067627 #7 May 08 2019 12:31:54
%S A067627 1,1,1,1,1,2,3,1,1,3,2,1,6,1,3,7,2,5,9,2,1,8,11,2,1,13,14,1,3,19,15,3,
%T A067627 5,27,19,1,11,34,22,2,1,15,49,23,2,1,27,59,28,3,3,39,78,30,1,5,60,93,
%U A067627 34,3,11,82,118,36,1,18,115,140,41,3,1,30,155,170,42,2,1,48
%N A067627 Triangle T(n,k) = number of conjugacy classes of partitions of n using only k types of piles, read by rows.
%C A067627 Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).
%e A067627 Triangle turned on its side begins:
%e A067627 1.1.1.2.1.2.1.2.2..2..1..3..1..2..2....etc A038548
%e A067627 ....1.1.3.3.6.7.9.11.14.15.19.22.23....etc A270060
%e A067627 ..........1.1.3.5..8.13.19.27.34.49....etc
%e A067627 ...................1..1..3..5.11.15....etc
%p A067627 compareL := proc(L1,L2)
%p A067627     if nops(L1) < nops(L2) then
%p A067627         -1 ;
%p A067627     elif nops(L1) > nops(L2) then
%p A067627         1;
%p A067627     else
%p A067627         for i from 1 to nops(L1) do
%p A067627             if op(i,L1) > op(i,L2) then
%p A067627                 return 1 ;
%p A067627             elif op(i,L1) < op(i,L2) then
%p A067627                 return -1 ;
%p A067627             end if;
%p A067627         end do:
%p A067627         0 ;
%p A067627     end if;
%p A067627 end proc:
%p A067627 A067627 := proc(n,k)
%p A067627     local a,p,s,pc ;
%p A067627     a := 0 ;
%p A067627     for p in combinat[partition](n) do
%p A067627         s := convert(p,set) ;
%p A067627         if nops(s) = k then
%p A067627             pc := combinat[conjpart](p) ;
%p A067627             if compareL(p,pc) <= 0 then
%p A067627                 a := a+1 ;
%p A067627             end if;
%p A067627         end if;
%p A067627     end do:
%p A067627     a ;
%p A067627 end proc:
%p A067627 for n from 1 to 30 do
%p A067627 for k from A003056(n) to 1 by -1 do
%p A067627     printf("%4d,",A067627(n,k)) ;
%p A067627 end do:
%p A067627 printf("\n") ;
%p A067627 end do: # _R. J. Mathar_, May 08 2019
%Y A067627 Cf. A000700, A000701, A046682, A060177. Diagonals give A038548. row sums give A046682.
%K A067627 easy,nonn,tabf
%O A067627 1,6
%A A067627 _Naohiro Nomoto_, Feb 02 2002
%E A067627 More terms from _R. J. Mathar_, May 08 2019