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A108950
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Number of partitions of n with more odd parts than even parts.
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6
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1, 1, 2, 3, 4, 7, 9, 14, 18, 27, 35, 49, 64, 86, 113, 148, 192, 247, 319, 404, 517, 649, 822, 1024, 1285, 1590, 1979, 2436, 3007, 3682, 4515, 5501, 6703, 8131, 9851, 11899, 14344, 17252, 20703, 24804, 29640, 35377
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) = A130780(n) - A045931(n) = A171967(n) - A108949(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 21 2010]
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FORMULA
| G.f.: Sum_{k>=0} x^k*(1-x^(2*k))/Product_{i=1..k} (1-x^(2*i))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2007
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EXAMPLE
| a(4)=3:{[3,1],[2,1,1],[1,1,1,1]};a(5)=4:{[5],[3,1,1],[2,1,1,1],[1,1,1,1,1]}
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MAPLE
| with(combinat, partition):oddbigrevn:=proc(n::nonnegint) local evencount, oddcount, bigcount, parts, i, j; printlevel:=-1; bigcount:=0; partitions:=partition(n); for i from 1 to nops(partitions) do evencount:=0; oddcount:=0; for j from 1 to nops(partitions[i]) do if (op(j, partitions[i]) mod 2 <>0) then oddcount:=oddcount+1 fi; if (op(j, partitions[i]) mod 2 =0) then evencount:=evencount+1 fi od; if (evencount<oddcount) then bigcount:=bigcount+1 fi od; printlevel:=1; return(bigcount) end proc; seq(oddbigrevn(i), i=1..42);
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CROSSREFS
| Cf. A045931 for #even parts = #odd parts, A108949 for #even parts > #odd parts.
Cf. A171966, A171967. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 21 2010]
Sequence in context: A139078 A065046 A049709 * A094093 A108809 A027947
Adjacent sequences: A108947 A108948 A108949 * A108951 A108952 A108953
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KEYWORD
| nonn
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AUTHOR
| Len Smiley ( smiley (AT) math.uaa.alaska.edu ), Jul 21 2005
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