OFFSET
0,1
COMMENTS
Subsequence of A088966.
For n > 1, number of connected dominating sets in the n-book graph. - Eric W. Weisstein, Jun 29 2017
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 0..100
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Connected Dominating Set
Index entries for linear recurrences with constant coefficients, signature (6, -8).
FORMULA
G.f.: 1/(1-4*x) + 2/(1-2*x). - Robert Israel, Aug 17 2014
E.g.f.: exp(4*x) + 2*exp(2*x). - G. C. Greubel, Jan 11 2020
EXAMPLE
a(0) = 4^0 + 2^1 = 1 + 2 = 3.
MAPLE
seq( 4^n + 2^(n+1), n=0..30); # G. C. Greubel, Jan 11 2020
MATHEMATICA
(* From Eric W. Weisstein, Jun 29 2017: (Start) *)
Table[4^n + 2^(n+1), {n, 0, 30}]
LinearRecurrence[{6, -8}, {8, 24}, {0, 30}]
CoefficientList[Series[(3-10x)/((1-2x)(1-4x)), {x, 0, 30}], x] (* End *)
PROG
(PARI) a(n) = 4^n + 2^(n+1);
(Magma) [4^n + 2^(n+1): n in [0..30]]; // G. C. Greubel, Jan 11 2020
(Sage) [4^n + 2^(n+1) for n in (0..30)] # G. C. Greubel, Jan 11 2020
(GAP) List([0..30], n-> 4^n + 2^(n+1)); # G. C. Greubel, Jan 11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 17 2014
STATUS
approved