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A242985
a(n) = 4^n + 2^(n+1).
2
3, 8, 24, 80, 288, 1088, 4224, 16640, 66048, 263168, 1050624, 4198400, 16785408, 67125248, 268468224, 1073807360, 4295098368, 17180131328, 68720001024, 274878955520, 1099513724928, 4398050705408, 17592194433024, 70368760954880, 281475010265088, 1125899973951488
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
FORMULA
a(n) = A000302(n) + A000079(n+1).
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