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 A084842 Number of rooted trees with n nodes with a height of 2 and with at least 1 node at height 1 has degree > 2. 0
 1, 2, 4, 7, 11, 17, 25, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS For n=9 we have the following valid graphic partitions; 9,82,73,64,55,443,533,542,632,722,3333,4332,4422,5322,43222. The basic pattern is partitions of n+k into k+1 parts, minimum part 2. After checking a graph can be produced (e.g. 6222 cannot), adding the number of distinct elements in each pattern gives the sequence, except for (n-1)2, which is always 1 and only counting elements which are greater than or equal to the number of elements in a pattern (e.g. 722 only yields 1 possibility). So the patterns above yield 1,1,2,2,1,2,2,3,3,1,1,2,1,2,1, adding gives a(9)=25 LINKS CROSSREFS Cf. A004250. Sequence in context: A004250 A289060 A194805 * A289177 A249039 A280962 Adjacent sequences:  A084839 A084840 A084841 * A084843 A084844 A084845 KEYWORD nonn AUTHOR Jon Perry, Jul 12 2003 STATUS approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)