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A206559
Number of 9's in the last section of the set of partitions of n.
3
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, 152, 187, 236, 289, 365, 442, 551, 671, 825, 999, 1226, 1474, 1796, 2159, 2609, 3124, 3765, 4485, 5377, 6396, 7627, 9041, 10750, 12696, 15038, 17724, 20909
OFFSET
1,13
COMMENTS
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.
FORMULA
It appears that A000041(n) = Sum_{j=1..9} a(n+j), n >= 0.
PROG
(Sage) A206559 = lambda n: sum(list(p).count(9) for p in Partitions(n) if 1 not in p)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 09 2012
STATUS
approved