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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A206560 Number of 10's in the last section of the set of partitions of n. 6 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 14, 22, 25, 36, 43, 59, 70, 95, 113, 150, 179, 232, 278, 356, 426, 537, 644, 803, 960, 1189, 1417, 1739, 2072, 2523, 2999, 3631, 4304, 5181, 6130, 7342, 8662, 10330, 12159, 14437, 16958 (list; graph; refs; listen; history; text; internal format) OFFSET 1,14 COMMENTS Zero together with the first differences of A024794. Also number of occurrences of 10 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 ten 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..10} a(n+j), n >= 0. PROG (Sage) A206560 = lambda n: sum(list(p).count(10) for p in Partitions(n) if 1 not in p) CROSSREFS Column 10 of A182703 and of A194812. Cf. A000041, A135010, A138121, A182712-A182714, A206555-A206559. Sequence in context: A239835 A361860 A026929 * A035554 A183567 A222710 Adjacent sequences: A206557 A206558 A206559 * A206561 A206562 A206563 KEYWORD nonn AUTHOR Omar E. Pol, Feb 09 2012 STATUS approved

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Last modified August 17 21:11 EDT 2024. Contains 375227 sequences. (Running on oeis4.)