id:A131889 - OEIS Search Results

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a(n) is the number of shapes of balanced trees with constant branching factor 3 and n nodes. The node is balanced if the size, measured in nodes, of each pair of its children differ by at most one node.

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5

1, 3, 3, 1, 9, 27, 27, 81, 81, 27, 27, 9, 1, 27, 243, 729, 6561, 19683, 19683, 59049, 59049, 19683, 177147, 531441, 531441, 1594323, 1594323, 531441, 531441, 177147, 19683, 59049, 59049, 19683, 19683, 6561, 729, 243, 27, 1 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`a(n) is always an integer power of 3.`
	LINKS	`Jeffrey A. Barnett Counting Balanced Tree Shapes.`
	FORMULA	`a(0) = a(1) = 1; a(3n+1+m) = (3 choose m) * a(n+1)^m * a(n)^(3-m), where n >= 0 and 0 <= m <= 3.`
	CROSSREFS	`Cf. A110316, A131890, A131891, A131892, A131893.` `Sequence in context: A108075 A084145 A122919 this_sequence A050609 A120870 A010029` `Adjacent sequences: A131886 A131887 A131888 this_sequence A131890 A131891 A131892`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jeffrey A. Barnett (jbb(AT)notatt.com), Jul 24 2007`

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.

AT&T Labs Research