OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 889
Index entries for linear recurrences with constant coefficients, signature (4,-3).
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) = 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
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 08 2000
STATUS
approved