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A067693 Minimum length of the self-conjugates partitions of n (0 if n=2; length of a partition is the number of parts). 0
0, 1, 0, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 4, 5, 4, 4, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

There are no self-conjugate partitions of 2, so we set a(2)=0.

LINKS

Table of n, a(n) for n=0..96.

EXAMPLE

a(12)=4 because the self-conjugate partitions of 12 are [6,2,1,1,1,1],[5,3,2,1,1] and [4,4,2,2], having 6,5 and 4 parts, respectively; the smallest is 4.

MAPLE

g:=sum(t^k*x^(k^2)/product(1-t*x^(2*j), j=1..k), k=1..15): gser:=simplify(series(g, x=0, 110)): 0, 1, 0, seq(ldegree(coeff(gser, x^n)), n=3..105); # sum(t^k*x^(k^2)/product(1-t*x^(2*j), j=1..k), k=1..infinity) is the bivariate g.f. for self-conjugate partitions according to weight (i.e. sum of the parts, marked by x) and number of parts (marked by t); - Emeric Deutsch, Apr 05 2006

CROSSREFS

Cf. A000700, A047993.

Sequence in context: A189025 A236347 A045430 * A322006 A173419 A099053

Adjacent sequences:  A067690 A067691 A067692 * A067694 A067695 A067696

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Feb 25 2002

EXTENSIONS

More terms from Emeric Deutsch, Apr 05 2006

STATUS

approved

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Last modified August 24 18:52 EDT 2019. Contains 326295 sequences. (Running on oeis4.)