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A206558 Number of 8's in the last section of the set of partitions of n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

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

PROG

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

CROSSREFS

Column 8 of A182703 and of A194812.

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

Sequence in context: A051754 A108747 A116931 * A145810 A172148 A205478

Adjacent sequences:  A206555 A206556 A206557 * A206559 A206560 A206561

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 09 2012

STATUS

approved

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Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)