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A117535
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Number of ways of writing n as a sum of powers of 3, each power being used at most 4 times.
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0
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1, 1, 2, 2, 1, 2, 2, 1, 3, 3, 2, 4, 4, 2, 3, 3, 1, 3, 3, 2, 4, 4, 2, 3, 3, 1, 4, 4, 3, 6, 6, 3, 5, 5, 2, 6, 6, 4, 8, 8, 4, 6, 6, 2, 5, 5, 3, 6, 6, 3, 4, 4, 1, 4, 4, 3, 6, 6, 3, 5, 5, 2, 6, 6, 4, 8, 8, 4, 6, 6, 2, 5, 5, 3, 6, 6, 3, 4, 4, 1, 5, 5, 4, 8, 8, 4, 7, 7, 3, 9, 9, 6, 12, 12, 6, 9, 9, 3, 8, 8, 5, 10, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| It seems that this sequence can be calculated by constructing an insertion tree in which the insertion rules depend on the "age" of a term at a particular stage of the calculation. See the link for a discussion of this concept.
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LINKS
| John W. Layman, Sequences Generated by Age-Determined Insertion Trees
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FORMULA
| G.f.=-1+product((1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))+x^(4*(3^j))), j=0..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2006
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EXAMPLE
| a(12)=4 because 12=9+3=9+1+1+1=3+3+3+3=3+3+3+1+1+1.
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MAPLE
| g:=-1+product((1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))+x^(4*(3^j))), j=0..10): gser:=series(g, x=0, 106): seq(coeff(gser, x, n), n=1..103); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2006
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CROSSREFS
| Cf. A054390.
Sequence in context: A123369 A178306 A023671 * A072463 A128853 A136165
Adjacent sequences: A117532 A117533 A117534 * A117536 A117537 A117538
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Mar 27 2006
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