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 A179009 Maximally refined partitions of n into distinct parts. 5
 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 3, 5, 1, 3, 2, 3, 5, 7, 2, 5, 3, 4, 6, 7, 11, 3, 8, 5, 6, 6, 8, 11, 15, 7, 13, 9, 9, 9, 10, 12, 16, 22, 11, 20, 15, 17, 14, 15, 16, 18, 24, 30, 18, 30, 26, 28, 22, 27, 21, 25, 27, 33, 42, 36, 45, 43, 46, 38, 44, 33, 43, 36, 44, 47, 60, 46, 66, 64, 70, 63, 72, 61, 69, 60, 63, 58, 69, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Let a_1,a_2,...,a_k be a partition of n into distinct parts. We say that this partition can be refined if one of the summands, say a_i can be replaced with two numbers whose sum is a_i  and the resulting partition is a partition into distinct parts.  For example, the partition 5+2 can be refined because 5 can be replaced by 4+1 to give 4+2+1.  If a partition into distinct parts cannot be refined we say that it is maximally refined. The value of a(0) is taken to be 1 as is often done when considering partitions (also, the empty partition cannot be refined). This sequence was suggested by Moshe Shmuel Newman. LINKS Joerg Arndt: C program to compute such partitions. EXAMPLE a(11)=2 because there are two partitions of 11 which are maximally refined, namely 6+4+1 and 5+3+2+1. CROSSREFS Sequence in context: A290267 A240750 A181118 * A112757 A219794 A286334 Adjacent sequences:  A179006 A179007 A179008 * A179010 A179011 A179012 KEYWORD nonn AUTHOR David S. Newman, Jan 03 2011 EXTENSIONS More terms from Joerg Arndt, Jan 04 2011 STATUS approved

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