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 A066639 Number of partitions of n with floor(n/2) parts. 1

%I

%S 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,

%T 101,134,135,175,176,230,231,296,297,384,385,489,490,626,627,791,792,

%U 1001,1002,1254,1255,1574,1575,1957,1958,2435,2436,3009,3010,3717,3718,4564

%N Number of partitions of n with floor(n/2) parts.

%F a(n)=A000041(ceiling(n/2))-1/2+(-1)^n/2 - _Benoit Cloitre_, Apr 28 2003

%e 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).

%p 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 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);

%o (PARI) a(n)=polcoeff(1/eta(x),ceil(n/2))-n%2

%K nonn

%O 1,4

%A _Amarnath Murthy_, Dec 28 2001

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 18 2003 and Apr 21 2003

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