A206555 Number of 5's in the last section of the set of partitions of n.

0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 4, 5, 8, 10, 15, 18, 26, 32, 44, 56, 73, 92, 120, 149, 193, 238, 302, 373, 469, 576, 716, 876, 1081, 1316, 1615, 1954, 2383, 2875, 3483, 4188, 5048, 6043, 7253, 8653, 10341, 12293, 14634, 17340, 20567, 24300, 28717, 33830

Offset: 1

Author

Omar E. Pol, Feb 09 2012

Keywords

• nonn

Comments

Zero together with the first differences of A024789. Also number of occurrences of 5 in all partitions of n that do not contain 1 as a part. It appears that the sum of five successive terms gives the partition numbers A000041 (see A182703 and A194812).

Crossrefs

Column 5 of A182703 and of A194812.

Cf. A135010, A138121, A182712-A182714.

Programs

Sage

A206555 = lambda n: sum(list(p).count(5) for p in Partitions(n) if 1 not in p)

Formula

It appears that A000041(n) = Sum_{j=1..5} a(n+j), n >= 0.

Extensions

More terms from Alois P. Heinz, Feb 20 2012