A206556 - OEIS

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A206556

Number of 6's in the last section of the set of partitions of n.

0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 5, 4, 8, 9, 14, 16, 26, 28, 42, 50, 69, 82, 114, 133, 179, 215, 279, 335, 434, 516, 657, 789, 987, 1182, 1473, 1754, 2164, 2583, 3154, 3755, 4567, 5414, 6542, 7753, 9307, 11000, 13158, 15501, 18456, 21712, 25731, 30196, 35677

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

COMMENTS

Zero together with the first differences of A024790. Also number of occurrences of 6 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 six 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..6} a(n+j), n >= 0.

PROG

(Sage) A206556 = lambda n: sum(list(p).count(6) for p in Partitions(n) if 1 not in p)

CROSSREFS

Column 6 of A182703 and of A194812.

Cf. A000041, A135010, A138121, A182712-A182714, A206556-A206560.

Sequence in context: A088880 A008818 A089599 * A127683 A127686 A293548

Adjacent sequences: A206553 A206554 A206555 * A206557 A206558 A206559

KEYWORD

nonn

AUTHOR

Omar E. Pol, Feb 09 2012

STATUS

approved