A348237 Coordination sequence for the cpq net with respect to a node where a hexagon and two octagons meet.

1, 3, 6, 9, 10, 13, 18, 21, 22, 23, 28, 33, 34, 35, 38, 43, 46, 47, 50, 53, 56, 59, 62, 65, 66, 69, 74, 77, 78, 79, 84, 89, 90, 91, 94, 99, 102, 103, 106, 109, 112, 115, 118, 121, 122, 125, 130, 133, 134, 135, 140, 145, 146, 147, 150, 155, 158, 159, 162, 165, 168, 171, 174

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

Cf. A348227-A348239.

Sequence in context: A289130 A188299 A187577 * A111359 A359352 A274428

Adjacent sequences: A348234 A348235 A348236 * A348238 A348239 A348240

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 10 2021

Status

approved