A067693 Minimum length of the self-conjugates partitions of n (0 if n=2; length of a partition is the number of parts).

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

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