A206559 - OEIS

%I #24 Dec 01 2013 13:35:02

%S 0,0,0,0,0,0,0,0,1,0,1,1,2,2,4,4,7,9,12,15,22,26,36,45,59,73,97,117,

%T 152,187,236,289,365,442,551,671,825,999,1226,1474,1796,2159,2609,

%U 3124,3765,4485,5377,6396,7627,9041,10750,12696,15038,17724,20909

%N Number of 9's in the last section of the set of partitions of n.

%C Zero together with the first differences of A024793. Also number of occurrences of 9 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 nine successive terms give the partition numbers A000041.

%F It appears that A000041(n) = Sum_{j=1..9} a(n+j), n >= 0.

%o (Sage) A206559 = lambda n: sum(list(p).count(9) for p in Partitions(n) if 1 not in p)

%Y Column 9 of A182703 and of A194812.

%Y Cf. A000041, A135010, A138121, A182712-A182714, A206555-A206558, A206560.

%K nonn

%O 1,13

%A _Omar E. Pol_, Feb 09 2012