OFFSET
0,2
COMMENTS
a(n) is the least number of nodes in a height-n 2-3-4 tree, if using the top-down insertion algorithm and there have been no deletions. - Daniel S. Roche, Oct 05 2014
Also the number of independent vertex sets and vertex covers in the n-crown graph. - Andrew Howroyd, May 14 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: (1-2*x^2)/((1-x)^2*(1-2*x)).
a(n) = 2*a(n-1) + 3 - n.
Row sums of A130301. - Gary W. Adamson, May 20 2007
MATHEMATICA
Table[2^(n + 1) + n - 1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)
LinearRecurrence[{4, -5, 2}, {4, 9, 18}, {0, 20}] (* Eric W. Weisstein, Sep 21 2017 *)
CoefficientList[Series[(-1 + 2 x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 21 2017 *)
PROG
(PARI) a(n)=if(n<0, 0, 2^(n+1)+n-1)
(Magma) [2^(n+1)+n-1: n in [0..35]]; // Vincenzo Librandi, Jul 20 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 15 2003
STATUS
approved