A206557 -id:A206557 - cp's OEIS frontend

A206558 Number of 8's in the last section of the set of partitions of n.

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 8, 8, 13, 15, 23, 26, 38, 45, 63, 74, 101, 120, 160, 191, 248, 298, 383, 457, 579, 694, 868, 1038, 1287, 1536, 1890, 2251, 2746, 3267, 3962, 4698, 5665, 6706, 8043, 9496, 11337, 13354, 15876, 18657, 22089

Offset: 1

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Omar E. Pol, Feb 09 2012

nonn

Zero together with the first differences of A024792. Also number of occurrences of 8 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 eight successive terms give the partition numbers A000041.

Column 8 of A182703 and of A194812.

Cf. A000041, A135010, A138121, A182712-A182714, A206555- A206557, A206559, A206560.

A206558 = lambda n: sum(list(p).count(8) for p in Partitions(n) if 1 not in p)

It appears that A000041(n) = Sum_{j=1..8} a(n+j), n >= 0.

cp's OEIS Frontend

A206558 Number of 8's in the last section of the set of partitions of n.

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