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A066639
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Number of partitions of n with floor(n/2) parts.
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1
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0, 1, 1, 2, 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 21, 22, 29, 30, 41, 42, 55, 56, 76, 77, 100, 101, 134, 135, 175, 176, 230, 231, 296, 297, 384, 385, 489, 490, 626, 627, 791, 792, 1001, 1002, 1254, 1255, 1574, 1575, 1957, 1958, 2435, 2436, 3009, 3010, 3717, 3718, 4564
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OFFSET
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1,4
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LINKS
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FORMULA
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EXAMPLE
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a(7)=4 as floor(7/2)=3 and the three-element partitions of 7 are (5, 1, 1), (4, 2, 1), (3, 3, 1), (3, 2, 2).
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MAPLE
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P := proc(n, k) option remember: if(k=1) then RETURN(1) elif(k<1 or n<1 or k>n) then RETURN(0) else RETURN(P(n-1, k-1)+P(n-k, k)) fi:end; seq(P(n, floor(n/2)), n=1..60);
P := proc(n, k) option remember: if(k<1 or n<1 or k>n) then RETURN(0) elif(k=1) then RETURN(1) else RETURN(P(n-1, k-1)+P(n-k, k)) fi:end; seq(P(n, floor(n/2)), n=1..60);
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PROG
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(PARI) a(n)=polcoeff(1/eta(x), ceil(n/2))-n%2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003 and Apr 21 2003
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STATUS
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approved
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