OFFSET
0,2
COMMENTS
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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also on arXiv, arXiv:1803.08530 [math.CO], 2018-2019.
Reticular Chemistry Structure Resource (RCSR), The cpq tiling (or net)
N. J. A. Sloane, A portion of the cpq net (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).
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,0,1,-1,1,-1).
FORMULA
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.)
MATHEMATICA
LinearRecurrence[{1, -1, 1, 0, 1, -1, 1, -1}, {1, 3, 6, 9, 10, 13, 18, 21, 22}, 100] (* Paolo Xausa, Feb 28 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 10 2021
STATUS
approved