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

1,1

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

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

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]

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).

Sequence in context: A128237 A176311 A036750 * A058748 A049314 A295505

Adjacent sequences: A286180 A286181 A286182 * A286184 A286185 A286186

Keyword

nonn

Author

Giovanni Resta, May 04 2017

Extensions

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

Status

approved