A286185 - OEIS

%I #25 May 21 2017 07:26:06

%S 3,15,55,173,511,1451,4019,10937,29371,78055,205679,538149,1399607,

%T 3621315,9327723,23931633,61186163,155949119,396369831,1004904733,

%U 2541896559,6416348251,16165611043,40657256617,102090514731,255968753175,640899345631,1602640560533

%N Number of connected induced (non-null) subgraphs of the Möbius ladder graph with 2n nodes.

%H Andrew Howroyd, <a href="/A286185/b286185.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Möbius Ladder</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>

%F a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6), for n>6 (conjectured).

%F a(n) = 1/4*((1-sqrt(2))^n*(4-3*sqrt(2)*n) + (1+sqrt(2))^n*(4+3*sqrt(2)*n)) - 1 - n (conjectured). - _Eric W. Weisstein_, May 08 2017

%F a(n) = Lucas(n, 2) + 3*n*Fibonacci(n, 2) - n - 1, where Lucas(n, 2) = A002203(n) and Fibonacci(n, 2) = A000129(n) (conjectured). - _Eric W. Weisstein_, May 08 2017

%F G.f. (subject to the above conjectures. In fact all three conjectures are equivalent): (3*x-3*x^2-2*x^3-4*x^4+3*x^5-x^6)/(1-3*x+x^2+x^3)^2. - _Robert Israel_, May 08 2017

%t a[n_] := Block[{g = CirculantGraph[2 n, {1, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n]}]]; Array[a, 8]

%Y Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).

%K nonn

%O 1,1

%A _Giovanni Resta_, May 04 2017

%E a(17)-a(28) from _Andrew Howroyd_, May 20 2017