A067731 Maximum number of distinct parts in a self-conjugate partition of n, or 0 if n=2.

0, 1, 0, 2, 1, 2, 3, 2, 3, 2, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 12, 11, 12, 11, 12, 11, 12, 11, 12, 11

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..87.

Formula

a(n) = r - (s mod 2), where n = r(r+1)/2 + s with 0 <= s <= r; i.e. r = floor((sqrt(8n+1)-1)/2).

Mathematica

r[n_] := Floor[(Sqrt[8n+1]-1)/2]; s[n_] := n-r[n](r[n]+1)/2; a[n_] := r[n]-Mod[s[n], 2]

Crossrefs

Cf. A000700, A067694.

Sequence in context: A006641 A191408 A115756 * A147844 A291985 A317192

Adjacent sequences: A067728 A067729 A067730 * A067732 A067733 A067734

Keyword

easy,nonn

Author

Naohiro Nomoto, Feb 05 2002

Extensions

Edited by Dean Hickerson, Feb 15 2002

Status

approved