OFFSET
0,2
COMMENTS
Binomial transform of A001045(n)+1.
For n > 1, also the number of independent vertex sets in the (n-1)-book graph. - Eric W. Weisstein, Aug 16 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Index entries for linear recurrences with constant coefficients, signature (5,-6).
FORMULA
a(n) = (3*2^n + 3^n - 0^n)/3.
a(n) = 2^n + 3^(n-1) for n >= 1.
G.f.: (1 - 2*x - 2*x*x)/((1 - 2*x)*(1 - 3*x)).
a(n) = 5*a(n-1) - 6*a(n-2) for n > 1. - Vincenzo Librandi, Sep 12 2014
E.g.f.: (1/3)*(exp(3*x) + 3*exp(2*x) -1). - G. C. Greubel, Aug 17 2017
MAPLE
seq(2^n + (3^n - charfcn[0](n))/3, n=0..100); # Robert Israel, Sep 12 2014
MATHEMATICA
CoefficientList[Series[(1 - 2 x - 2 x^2)/((1 - 2 x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 12 2014 *)
Join[{1}, LinearRecurrence[{5, -6}, {3, 7}, 20]] (* Eric W. Weisstein, Aug 16 2017 *)
Join[{1}, Table[2^n + 3^(n - 1), {n, 20}]] (* Eric W. Weisstein, Aug 16 2017 *)
PROG
(Magma) [1] cat [2^n+3^(n-1): n in [1..30]]; // Vincenzo Librandi, Sep 12 2014
(PARI) Vec((1-2*x-2*x*x)/((1-2*x)*(1-3*x)) + O(x^50)) \\ Michel Marcus, Sep 12 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 25 2003
STATUS
approved