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A054390
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Number of ways of writing n as a sum of powers of 3, each power being used at most three times.
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2
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1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 5, 4, 4, 7, 3, 3, 6, 3, 3, 8, 5, 5, 7, 2, 2, 4, 2, 2, 6, 4, 4, 6, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 14 2010: (Start)
Let M = an infinite matrix with (1, 1, 1, 1, 0, 0, 0,...) in each column
shifted down thrice from the previous column (for k>0). Then A054390 =
Lim_{n->inf} M^n, the left-shifted vector considered as a sequence. (End)
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FORMULA
| a(0)=1, a(1)=1, a(2)=1 and, for n>0, a(3n)=a(n)+a(n-1), a(3n+1)=a(n), a(3n+2)=a(n).
G.f.=product((1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))), j=0..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2006
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EXAMPLE
| a(33)=4 because we have 33=27+3+3=27+3+1+1+1=9+9+9+3+3=9+9+9+3+1+1+1.
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MAPLE
| a[0]:=1: a[1]:=1: a[2]:=1: for n from 1 to 35 do a[3*n]:=a[n]+a[n-1]: a[3*n+1]:=a[n]: a[3*n+2]:=a[n] od: A:=[seq(a[n], n=0..104)]; - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2006
g:=product((1+x^(3^j)+x^(2*(3^j))+x^(3*(3^j))), j=0..10): gser:=series(g, x=0, 125): seq(coeff(gser, x, n), n=0..104); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 02 2006
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CROSSREFS
| Cf. A002487.
Sequence in context: A067594 A089533 A184241 * A161068 A161107 A161042
Adjacent sequences: A054387 A054388 A054389 * A054391 A054392 A054393
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), May 09 2000
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