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A052909 Expansion of g.f. (1+x-x^2)/((1-x)*(1-3*x)). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 3*a(n-1) + 1, with a(0)=1, a(1)=5, a(2)=16.
a(n) = (11*3^n - 3)/6.
a(n) = 4*a(n-1) - 3*a(n-2). - Vincenzo Librandi, Jun 22 2012
a(n+1) = A237930(n) + 2*A000244(n). - Philippe Deléham, Feb 17 2014
a(n) = Sum_{k=1..3} floor((3^n)/k). - Lechoslaw Ratajczak, Jul 31 2016
E.g.f.: (11*exp(3*x) - 3*exp(x) - 2)/6. - Stefano Spezia, Aug 28 2023
EXAMPLE
Ternary.......................Decimal
1...................................1
12..................................5
121................................16
1211...............................49
12111.............................148
121111............................445
1211111..........................1336
12111111.........................4009
121111111.......................12028
1211111111......................36085, etc. - Philippe Deléham, Feb 17 2014
MAPLE
spec := [S, {S=Prod(Union(Sequence(Z), Z), Sequence(Union(Z, Z, Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A171426 A180129 A244410 * A037536 A192904 A082001
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 08 2000
STATUS
approved

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Last modified February 20 20:53 EST 2024. Contains 370217 sequences. (Running on oeis4.)