0,7

By removing a single part of size 3, an A026796 partition of n becomes an A008483 partition of n - 3.

For n >= 3 the sequence counts the isomorphism classes of authentication codes AC(2,n,n) with perfect secrecy and with largest probability 0.5 that an interceptor could deceive with a substituted message.

Also the number of regular graphs of degree 2. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 22, 2005.

R.-Q. Feng, J. H. Kwak and E. K. Lloyd, Isomorphism classes of authentication codes, Bull. Austral. Math. Soc. 69 (2004), no. 2, 203-215.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 446

p(n) - p(n - 1) - p(n - 2) + p(n - 3) where p(n) is the number of unrestricted partitions of n into positive parts (A000041).

G.f.: Product 1/(1-x^m); m=3..inf.

a(n) = A121081(n+3) - A121659(n+3). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 14 2006

series(1/product((1-x^i), i=3..50), x, 51);

ZL := [ B, {B=Set(Set(Z, card>=3))}, unlabeled ]: seq(combstruct[count](ZL, size=n), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007

with(combstruct):ZL2:=[S, {S=Set(Cycle(Z, card>2))}, unlabeled]:seq(count(ZL2, size=n), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007

with (combstruct):a:=proc(m) [A, {A=Set(Cycle(Z, card>m))}, unlabeled]; end: A008483:=a(2):seq(count(A008483, size=n), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

Essentially the same sequence as A026796.

Sequence in context: A091583 A132326 A027195 this_sequence A026796 A008925 A036072

Adjacent sequences: A008480 A008481 A008482 this_sequence A008484 A008485 A008486

nonn

T. Forbes (anthony.d.forbes(AT)googlemail.com)

Additional comments from E. Keith Lloyd (ekl(AT)soton.ac.uk).