A286183 Number of connected induced (non-null) subgraphs of the antiprism graph with 2n nodes.

3, 15, 60, 207, 663, 2038, 6107, 17983, 52272, 150407, 429223, 1216490, 3427635, 9609327, 26821668, 74576703, 206650167, 570877918, 1572754187, 4322192287, 11851474968, 32430381815, 88576465735, 241511251922, 657457204323, 1787147867343, 4851349002252

Offset: 1

Author

Giovanni Resta, May 04 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Crossrefs

Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).

Programs

Mathematica

a[n_] := Block[{g = Graph@ Flatten@ Table[{i <-> Mod[i,n]+1, n+i <-> Mod[i,n] + n+1, i <-> n + Mod[i, n] + 1, i <-> n + Mod[i-1, n] + 1}, {i, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n]}]]; Array[a, 8]

Formula

a(n) = 8*a(n-1) - 24*a(n-2) + 34*a(n-3) - 24*a(n-4) + 8*a(n-5) - a(n-6), for n > 6 (conjectured).

a(n) = A005248(n) - 2*n + 2*n*A001906(n) (conjectured). - Eric W. Weisstein, May 08 2017

G.f.: x*(3 - 9*x + 12*x^2 - 15*x^3 + 9*x^4 - 2*x^5) / ((1 - x)^2*(1 - 3*x + x^2)^2) (conjectured). - Colin Barker, May 30 2017

Extensions

a(17)-a(27) from Andrew Howroyd, May 20 2017