A206559 - OEIS

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A206559

Number of 9's in the last section of the set of partitions of n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 9, 12, 15, 22, 26, 36, 45, 59, 73, 97, 117, 152, 187, 236, 289, 365, 442, 551, 671, 825, 999, 1226, 1474, 1796, 2159, 2609, 3124, 3765, 4485, 5377, 6396, 7627, 9041, 10750, 12696, 15038, 17724, 20909

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OFFSET

1,13

COMMENTS

Zero together with the first differences of A024793. Also number of occurrences of 9 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 nine successive terms give the partition numbers A000041.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

It appears that A000041(n) = Sum_{j=1..9} a(n+j), n >= 0.

PROG

(Sage) A206559 = lambda n: sum(list(p).count(9) for p in Partitions(n) if 1 not in p)

CROSSREFS

Column 9 of A182703 and of A194812.

Cf. A000041, A135010, A138121, A182712-A182714, A206555-A206558, A206560.

Sequence in context: A256217 A361439 A055636 * A143419 A183566 A222709

Adjacent sequences: A206556 A206557 A206558 * A206560 A206561 A206562

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 09 2012

STATUS

approved