A206559 Number of 9's in the last section of the set of partitions of n.

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

Author

Omar E. Pol, Feb 09 2012

Keywords

• nonn

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.

Crossrefs

Column 9 of A182703 and of A194812.

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

Programs

Sage

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

Formula

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