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A238219 The total number of 4's in all partitions of n into an even number of distinct parts. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

The g.f. for "number of k's" is (1/2)*x^k/(1+x^k)*prod(n>=1,1+x^n)-(1/2)*x^k/(1-x^k)*prod(n>=1,1-x^n).

LINKS

Table of n, a(n) for n=0..50.

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)*prod(n>=1,1+x^n)-(1/2)*x^4/(1-x^4)*prod(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

Cf. A067659, A067661.

Sequence in context: A030383 A031231 A030562 * A026833 A281544 A056882

Adjacent sequences:  A238216 A238217 A238218 * A238220 A238221 A238222

KEYWORD

nonn

AUTHOR

Mircea Merca, Feb 20 2014

STATUS

approved

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Last modified August 25 21:00 EDT 2019. Contains 326324 sequences. (Running on oeis4.)