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A363251 Number of nonisomorphic open quipus with n nodes.

%I A363251 #34 Jan 13 2025 06:34:35
%S A363251 1,1,1,1,2,2,4,6,11,18,36,64,127,241,480,935,1868,3688,7373,14655,
%T A363251 29305,58432,116859,233367,466727,932761,1865513,3729648,7459286,
%U A363251 14915826,29831640,59657802,119315589,238620236,477240456,954459044,1908918069,3817792423
%N A363251 Number of nonisomorphic open quipus with n nodes.
%C A363251 An open quipu is a tree of maximal valency 3 such that all nodes of degree 3 lie on a path.
%H A363251 Paolo Xausa, <a href="/A363251/b363251.txt">Table of n, a(n) for n = 0..1000</a>
%H A363251 Renee Woo and Arnold Neumaier, <a href="https://doi.org/10.1007/s00373-007-0745-9">On Graphs Whose Spectral Radius is Bounded by 3/2*sqrt(2)</a>, Graphs and Combinatorics 23 (2007), 713-726. Also <a href="https://arnold-neumaier.at/papers.html#evmax">preprint and slides</a>.
%H A363251 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-5,-3,-1,3,7,0,-1,-6,-2,4).
%F A363251 G.f.: (1 - x - 4*x^2 + x^3 + 5*x^4 + 4*x^5 - 4*x^7 - 6*x^8 - 3*x^9 + 5*x^10 + 4*x^11 - x^12)/((1 - x)^3*(1 + x)^2*(1 - 2*x)*(1 + x^2)*(1 + x + x^2)*(1 - 2*x^2)). - _Andrew Howroyd_, May 31 2023
%e A363251 The 4 open quipus with 6 nodes are:
%e A363251   ._._._._._.   ._._._._.   ._._._._.   ._._._.
%e A363251                   |             |         | |
%e A363251 The smallest interesting nonexample, a 3-valent tree where the nodes of degree 3 do not lie on a path, is:
%e A363251      .   .
%e A363251      |   |
%e A363251    ._._._._.
%e A363251        |
%e A363251      ._._.
%t A363251 LinearRecurrence[{2,3,-5,-3,-1,3,7,0,-1,-6,-2,4},{1,1,1,1,2,2,4,6,11,18,36,64,127},50] (* _Paolo Xausa_, Aug 13 2023 *)
%Y A363251 A000672 minus the trees where the nodes of degree 3 do not lie on a path.
%Y A363251 Cf. A130131 (any maximum degree).
%K A363251 nonn,easy
%O A363251 0,5
%A A363251 _Didrik Fosse_, May 31 2023