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A286182
Number of connected induced (non-null) subgraphs of the prism graph with 2n nodes.
17
3, 13, 51, 167, 503, 1441, 4007, 10923, 29355, 78037, 205659, 538127, 1399583, 3621289, 9327695, 23931603, 61186131, 155949085, 396369795, 1004904695, 2541896519, 6416348209, 16165610999, 40657256571, 102090514683, 255968753125, 640899345579, 1602640560479
OFFSET
1,1
COMMENTS
Cases n=1 and n=2 correspond to degenerate prism graphs, but they fit the same (conjectured) linear recurrence as the other terms.
LINKS
Eric Weisstein's World of Mathematics, Prism Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
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).
a(n) = A002203(n) + 3*n*A000129(n) - 3*n + 1 (conjectured). - Eric W. Weisstein, May 08 2017
G.f.: x*(3 - 5*x + 6*x^2 - 8*x^3 - 5*x^4 - 3*x^5) / ((1 - x)^2*(1 - 2*x - x^2)^2) (conjectured). - Colin Barker, May 31 2017
MATHEMATICA
a[n_] := Block[{g = Graph@ Flatten@ Table[{i <-> Mod[i, n] + 1, n+i <-> Mod[i, n] + n+1, i <-> i+n}, {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), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).
Sequence in context: A026529 A363881 A357870 * A101052 A016064 A163774
KEYWORD
nonn
AUTHOR
Giovanni Resta, May 04 2017
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, Aug 15 2017
STATUS
approved