A206560 - OEIS

%I #21 Dec 01 2013 13:35:02

%S 0,0,0,0,0,0,0,0,0,1,0,1,1,2,2,4,4,7,8,13,14,22,25,36,43,59,70,95,113,

%T 150,179,232,278,356,426,537,644,803,960,1189,1417,1739,2072,2523,

%U 2999,3631,4304,5181,6130,7342,8662,10330,12159,14437,16958

%N Number of 10's in the last section of the set of partitions of n.

%C Zero together with the first differences of A024794. Also number of occurrences of 10 in all partitions of n that do not contain 1 as a part. For the definition of "last section of n" see A135010. It appears that the sums of ten successive terms give the partition numbers A000041.

%F It appears that A000041(n) = Sum_{j=1..10} a(n+j), n >= 0.

%o (Sage) A206560 = lambda n: sum(list(p).count(10) for p in Partitions(n) if 1 not in p)

%Y Column 10 of A182703 and of A194812.

%Y Cf. A000041, A135010, A138121, A182712-A182714, A206555-A206559.

%K nonn

%O 1,14

%A _Omar E. Pol_, Feb 09 2012