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 A286304 Number of connected induced (non-null) subgraphs of the complete binary tree with graph n nodes. 2
 1, 3, 6, 10, 17, 24, 37, 51, 78, 110, 173, 229, 340, 477, 750, 1024, 1571, 2253, 3616, 5024, 7839, 11356, 18389, 25173, 38740, 55697, 89610, 124870, 195389, 283536, 459829, 636123, 988710, 1429442, 2310905, 3227617, 5061040, 7352817, 11936370, 16526444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..5651 (first 255 terms from Andrew Howroyd) Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph Wikipedia, Types of binary trees FORMULA a(2^k-1) = A285934(k-1). MATHEMATICA Join[{1}, Table[g=KaryTree[n]; -1 + ParallelSum[Boole@ConnectedGraphQ@Subgraph[g, s], {s, Subsets@Range[n]}], {n, 2, 16}]] (* Second program: *) l[n_] := With[{h = 2^Floor[Log[2, n]]}, Min[h - 1, n - h/2]]; b[n_] := b[n] = 1 + If[n <= 1, n, b[l[n]]*b[n - 1 - l[n]]]; a[n_] := a[n] = If[n <= 1, n, b[n] - 1 + a[l[n]] + a[n - 1 - l[n]]]; Array[a, 40] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *) PROG (PARI) l(n)={my(h=2^floor(log(n)/log(2))); min(h-1, n-h/2)} b(n)=1+if(n<=1, n, b(l(n))*b(n-1-l(n))); a(n)=if(n<=1, n, b(n)-1 + a(l(n)) + a(n-1-l(n))); \\ Andrew Howroyd, May 22 2017 CROSSREFS Cf. A285934, A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen). Sequence in context: A094272 A236326 A308699 * A005045 A189376 A069241 Adjacent sequences:  A286301 A286302 A286303 * A286305 A286306 A286307 KEYWORD nonn AUTHOR Giovanni Resta, May 05 2017 EXTENSIONS Terms a(35) and beyond from Andrew Howroyd, May 22 2017 STATUS approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)