id:A117535 - OEIS Search Results

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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.

+0
1

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; listen)

	OFFSET	`1,3`
	COMMENT	`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.`
	LINKS	`John W. Layman, Sequences Generated by Age-Determined Insertion Trees`
	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`
	EXAMPLE	`a(12)=4 because 12=9+3=9+1+1+1=3+3+3+3=3+3+3+1+1+1.`
	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`
	CROSSREFS	`Cf. A054390.` `Sequence in context: A025260 A123369 A023671 this_sequence A072463 A128853 A136165` `Adjacent sequences: A117532 A117533 A117534 this_sequence A117536 A117537 A117538`
	KEYWORD	`nonn`
	AUTHOR	`John W. Layman (layman(AT)math.vt.edu), Mar 27 2006`

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Last modified November 18 20:14 EST 2008. Contains 147244 sequences.

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