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%I #31 Feb 28 2024 07:04:06
%S 1,3,6,9,10,13,18,21,22,23,28,33,34,35,38,43,46,47,50,53,56,59,62,65,
%T 66,69,74,77,78,79,84,89,90,91,94,99,102,103,106,109,112,115,118,121,
%U 122,125,130,133,134,135,140,145,146,147,150,155,158,159,162,165,168,171,174
%N Coordination sequence for the cpq net with respect to a node where a hexagon and two octagons meet.
%C The cpq net is the dual graph to the 123-circle graph G studied in A348227-A348235. Thanks to _Davide M. Proserpio_ for pointing this out.
%H Alois P. Heinz, <a href="/A348237/b348237.txt">Table of n, a(n) for n = 0..10000</a>
%H Chaim Goodman-Strauss and N. J. A. Sloane, <a href="https://doi.org/10.1107/S2053273318014481">A Coloring Book Approach to Finding Coordination Sequences</a>, Acta Cryst. A75 (2019), 121-134, also <a href="http://NeilSloane.com/doc/Cairo_final.pdf">on NJAS's home page</a>. Also <a href="http://arxiv.org/abs/1803.08530">on arXiv</a>, arXiv:1803.08530 [math.CO], 2018-2019.
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/cpq">The cpq tiling (or net)</a>
%H N. J. A. Sloane, <a href="/A348237/a348237.pdf">A portion of the cpq net</a> (the numbers correspond to the coordination sequence for nodes in the first quadrant, with respect to a base point in the lower left corner of the picture).
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,0,1,-1,1,-1).
%F G.f. = (1+q)*(1+q^3)*(q^4+q^3+3*q^2+q+1) / ((1-q)*(1+q^2)*(1-q^5)). (Discovered and proved using the "coloring book" method.)
%t LinearRecurrence[{1, -1, 1, 0, 1, -1, 1, -1}, {1, 3, 6, 9, 10, 13, 18, 21, 22}, 100] (* _Paolo Xausa_, Feb 28 2024 *)
%Y Cf. A348227-A348239.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 10 2021
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