A206560 Number of 10's in the last section of the set of partitions of n.

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, 150, 179, 232, 278, 356, 426, 537, 644, 803, 960, 1189, 1417, 1739, 2072, 2523, 2999, 3631, 4304, 5181, 6130, 7342, 8662, 10330, 12159, 14437, 16958

Offset: 1

Author

Omar E. Pol, Feb 09 2012

Keywords

• nonn

Comments

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.

Crossrefs

Column 10 of A182703 and of A194812.

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

Programs

Sage

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

Formula

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