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%I #11 Apr 29 2020 18:18:01
%S 0,0,0,0,0,0,1,1,1,1,0,2,2,2,3,3,5,6,7,8,9,12,14,16,19,22,27,31,36,42,
%T 48,56,65,75,86,99,114,130,149,170,193,220,250,283,321,364,410,463,
%U 522,587,661,742,832,933,1045,1169,1306,1459,1627,1814,2021
%N The total number of 5's in all partitions of n into an even number of distinct parts.
%C The g.f. for "number of k's" is (1/2)*(x^k/(1+x^k))*(Product_{n>=1} 1 + x^n) - (1/2)*(x^k/(1-x^k))*(Product_{n>=1} 1 - x^n).
%H Andrew Howroyd, <a href="/A238220/b238220.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{j=1..round(n/10)} A067659(n-(2*j-1)*5) - Sum_{j=1..floor(n/10)} A067661(n-10*j).
%F G.f.: (1/2)*(x^5/(1+x^5))*(Product_{n>=1} 1 + x^n) - (1/2)*(x^5/(1-x^5))*(Product_{n>=1} 1 - x^n).
%e a(13) = 2 because the partitions in question are: 8+5, 5+4+3+1.
%Y Column k=5 of A238451.
%Y Cf. A067659, A067661.
%K nonn
%O 0,12
%A _Mircea Merca_, Feb 20 2014
%E Terms a(51) and beyond from _Andrew Howroyd_, Apr 29 2020
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