A206555 - OEIS

%I #20 Nov 30 2013 21:30:38

%S 0,0,0,0,1,0,1,1,2,3,4,5,8,10,15,18,26,32,44,56,73,92,120,149,193,238,

%T 302,373,469,576,716,876,1081,1316,1615,1954,2383,2875,3483,4188,5048,

%U 6043,7253,8653,10341,12293,14634,17340,20567,24300,28717,33830

%N Number of 5's in the last section of the set of partitions of n.

%C Zero together with the first differences of A024789. Also number of occurrences of 5 in all partitions of n that do not contain 1 as a part. It appears that the sum of five successive terms gives the partition numbers A000041 (see A182703 and A194812).

%F It appears that A000041(n) = Sum_{j=1..5} a(n+j), n >= 0.

%o (Sage) A206555 = lambda n: sum(list(p).count(5) for p in Partitions(n) if 1 not in p)

%Y Column 5 of A182703 and of A194812.

%Y Cf. A135010, A138121, A182712-A182714.

%K nonn

%O 1,9

%A _Omar E. Pol_, Feb 09 2012

%E More terms from _Alois P. Heinz_, Feb 20 2012