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

1,9

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).

Links

Table of n, a(n) for n=1..52.

Formula

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

Prog

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

Crossrefs

Column 5 of A182703 and of A194812.

Cf. A135010, A138121, A182712-A182714.

Sequence in context: A240177 A035555 A039875 * A110539 A222297 A211981

Adjacent sequences: A206552 A206553 A206554 * A206556 A206557 A206558

Keyword

nonn

Author

Omar E. Pol, Feb 09 2012

Extensions

More terms from Alois P. Heinz, Feb 20 2012

Status

approved