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A238220
The total number of 5's in all partitions of n into an even number of distinct parts.
2
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, 48, 56, 65, 75, 86, 99, 114, 130, 149, 170, 193, 220, 250, 283, 321, 364, 410, 463, 522, 587, 661, 742, 832, 933, 1045, 1169, 1306, 1459, 1627, 1814, 2021
OFFSET
0,12
COMMENTS
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).
LINKS
FORMULA
a(n) = Sum_{j=1..round(n/10)} A067659(n-(2*j-1)*5) - Sum_{j=1..floor(n/10)} A067661(n-10*j).
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).
EXAMPLE
a(13) = 2 because the partitions in question are: 8+5, 5+4+3+1.
CROSSREFS
Column k=5 of A238451.
Sequence in context: A367395 A065308 A035680 * A103600 A267160 A374436
KEYWORD
nonn
AUTHOR
Mircea Merca, Feb 20 2014
EXTENSIONS
Terms a(51) and beyond from Andrew Howroyd, Apr 29 2020
STATUS
approved