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 A132843 a(n) = A005704( A037480(n) ) for n>0 with a(0)=1, where A005704 = number of partitions of 3n into powers of 3 and A037480(n) = n-th number having alternating base-3 digits 1, 2 (starting with '1'). 2
 1, 2, 9, 72, 1296, 52407, 5240052, 1314516033, 853923545352, 1457086698392796, 6631460154689418828, 81384300080656595328843, 2719577128999047606509974434, 249432083657086432899494832228657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..40 FORMULA a(n) = A005704( (5*3^n + (-1)^n - 6)/8 ). EXAMPLE Let b(n) = A005704(n) = number of partitions of 3n into powers of 3, then the initial terms of this sequence begin: b(0), b(1), b(5), b(16), b(50), b(151), b(455), b(1366),... APPLICATION: SPECIAL TERNARY TREE. a(n) = number of nodes in generation n of the following tree. Start at generation 0 with a single root node labeled . From then on, each parent node [k] is attached k child nodes with labels congruent to 2(mod 3) for even n, or 3(mod 3) for odd n, within the range {1..3k}, for generation n >= 0. The initial generations 0..3 of the tree begin as follows; the path from the root node is given, followed by child nodes in []. GEN.0: ; GEN.1: 2->[3,6]; GEN.2: 2-3->[2,5,8] 2-6->[2,5,8,11,14,17]; GEN.3: 2-3-2->[3,6] 2-3-5->[3,6,9,12,15] 2-3-8->[3,6,9,12,15,18,21,24] 2-6-2->[3,6] 2-6-5->[3,6,9,12,15] 2-6-8->[3,6,9,12,15,18,21,24] 2-6-11->[3,6,9,12,15,18,21,24,27,30,33] 2-6-14->[3,6,9,12,15,18,21,24,27,30,33,36,39,42] 2-6-17->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51] . Note: largest node label in generation n is A037480(n) + 1, and the sum of the labels in generation n equals a(n+1). PROG (PARI) {A005704(n) = if(n<1, n==0, A005704(n\3) + A005704(n-1))} {a(n) = A005704( (5*3^n + (-1)^n - 6)/8 )} CROSSREFS Cf. A005704, A037480; variant: A132880. Sequence in context: A208898 A108995 A184358 * A346648 A336955 A084873 Adjacent sequences:  A132840 A132841 A132842 * A132844 A132845 A132846 KEYWORD nonn,base AUTHOR Paul D. Hanna, Sep 27 2007 STATUS approved

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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)