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A067627
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Triangle T(n,k) = number of conjugacy classes of partitions of n using only k types of piles, read by rows.
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2
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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, 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, 34, 3, 11, 82, 118, 36, 1, 18, 115, 140, 41, 3, 1, 30, 155, 170, 42, 2, 1, 48
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OFFSET
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1,6
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COMMENTS
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Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).
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LINKS
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EXAMPLE
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Triangle turned on its side begins:
1.1.1.2.1.2.1.2.2..2..1..3..1..2..2....etc A038548
....1.1.3.3.6.7.9.11.14.15.19.22.23....etc A270060
..........1.1.3.5..8.13.19.27.34.49....etc
...................1..1..3..5.11.15....etc
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MAPLE
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compareL := proc(L1, L2)
if nops(L1) < nops(L2) then
-1 ;
elif nops(L1) > nops(L2) then
1;
else
for i from 1 to nops(L1) do
if op(i, L1) > op(i, L2) then
return 1 ;
elif op(i, L1) < op(i, L2) then
return -1 ;
end if;
end do:
0 ;
end if;
end proc:
local a, p, s, pc ;
a := 0 ;
for p in combinat[partition](n) do
s := convert(p, set) ;
if nops(s) = k then
pc := combinat[conjpart](p) ;
if compareL(p, pc) <= 0 then
a := a+1 ;
end if;
end if;
end do:
a ;
end proc:
for n from 1 to 30 do
for k from A003056(n) to 1 by -1 do
end do:
printf("\n") ;
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CROSSREFS
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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