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A052909
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Expansion of g.f. (1+x-x^2)/((1-x)*(1-3*x)).
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6
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1, 5, 16, 49, 148, 445, 1336, 4009, 12028, 36085, 108256, 324769, 974308, 2922925, 8768776, 26306329, 78918988, 236756965, 710270896, 2130812689, 6392438068, 19177314205, 57531942616, 172595827849, 517787483548, 1553362450645
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3*a(n-1) + 1, with a(0)=1, a(1)=5, a(2)=16.
a(n) = (11*3^n - 3)/6.
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EXAMPLE
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Ternary.......................Decimal
1...................................1
12..................................5
121................................16
1211...............................49
12111.............................148
121111............................445
1211111..........................1336
12111111.........................4009
121111111.......................12028
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MAPLE
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spec := [S, {S=Prod(Union(Sequence(Z), Z), Sequence(Union(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[(1+x-x^2)/((1-x)*(1-3*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 22 2012 *)
Join[{1}, (11*3^Range[30] -3)/6] (* G. C. Greubel, Oct 15 2019 *)
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PROG
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(Magma) I:=[1, 5, 16]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012
(PARI) vector(30, n, if(n==1, 1, (11*3^(n-1) - 3)/6)) \\ G. C. Greubel, Oct 15 2019
(Sage) [1]+[(11*3^n -3)/6 for n in (1..30)] # G. C. Greubel, Oct 15 2019
(GAP) Concatenation([1], List([1..30], n-> (11*3^n - 3)/6)); # G. C. Greubel, Oct 15 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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