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A238219
The total number of 4's in all partitions of n into an even number of distinct parts.
2
0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 2, 3, 4, 4, 5, 6, 8, 9, 11, 13, 16, 18, 21, 25, 29, 34, 40, 46, 53, 62, 71, 82, 94, 108, 124, 142, 161, 185, 210, 238, 270, 307, 347, 392, 442, 499, 562, 632, 709, 797, 894, 1000, 1119, 1252, 1398, 1560, 1739, 1937, 2157
OFFSET
0,11
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/8)} A067659(n-(2*j-1)*4) - Sum_{j=1..floor(n/8)} A067661(n-8*j).
G.f.: (1/2)*(x^4/(1+x^4))*(Product_{n>=1} 1 + x^n) - (1/2)*(x^4/(1-x^4))*(Product_{n>=1} 1 - x^n).
EXAMPLE
a(13) = 3 because the partitions in question are: 9+4, 6+4+2+1, 5+4+3+1.
CROSSREFS
Column k=4 of A238451.
Sequence in context: A030383 A031231 A030562 * A026833 A281544 A056882
KEYWORD
nonn
AUTHOR
Mircea Merca, Feb 20 2014
EXTENSIONS
Terms a(51) and beyond from Andrew Howroyd, Apr 29 2020
STATUS
approved