%I #15 Sep 08 2022 08:46:02

%S 1,3,6,13,26,54,110,225,456,922,1862,3755,7562,15214,30584,61441,

%T 123362,247581,496694,996148,1997288,4003654,8023886,16078166,

%U 32212255,64527754,129246702,258848476,518358122,1037950430,2078209982,4160749569,8329633544

%N 2^(n-1) - floor((2^(n-1) - 1)/(n-1)).

%C Lower bounds of the decycling numbers of n-cubes for n >= 9.

%H Arkadiusz Wesolowski, <a href="/A213255/b213255.txt">Table of n, a(n) for n = 2..800</a>

%H Sheng Bau, <a href="http://arxiv.org/abs/math/0703544">The Decycling Number of Graphs</a>

%F a(n) = 2^(n-1) - floor((2^(n-1) - 1)/(n-1)).

%F a(n) = ceiling(2^(n-1) - (2^(n-1) - 1)/(n-1)).

%e a(8) = 110 because 2^7 - (2^7 - 1)/7 = 109.8571428571....

%t Table[Ceiling[2^(n - 1) - (2^(n - 1) - 1)/(n - 1)], {n, 2, 34}]

%o (Magma) [Ceiling(2^(n-1)-(2^(n-1)-1)/(n-1)) : n in [2..34]]

%o (PARI) for(n=2, 34, print1(ceil(2^(n-1)-(2^(n-1)-1)/(n-1)), ", "))

%Y Cf. A005009.

%K easy,nonn

%O 2,2

%A _Arkadiusz Wesolowski_, Jun 07 2012