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A301718 Coordination sequence for node of type V2 in "kre" 2-D tiling (or net). 38
1, 5, 11, 17, 23, 28, 33, 39, 45, 51, 56, 61, 67, 73, 79, 84, 89, 95, 101, 107, 112, 117, 123, 129, 135, 140, 145, 151, 157, 163, 168, 173, 179, 185, 191, 196, 201, 207, 213, 219, 224, 229, 235, 241, 247, 252, 257, 263, 269, 275, 280, 285, 291, 297, 303, 308 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Linear recurrence and g.f. confirmed by Shutov/Maleev link. - Ray Chandler, Aug 30 2023
REFERENCES
Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 67, 1st row, 3rd tiling.
LINKS
Brian Galebach, Collection of n-Uniform Tilings. See Number 18 from the list of 20 2-uniform tilings.
Reticular Chemistry Structure Resource (RCSR), The kre tiling (or net)
Anton Shutov and Andrey Maleev, Coordination sequences of 2-uniform graphs, Z. Kristallogr., 235 (2020), 157-166. See supplementary material, krb, vertex u_1.
FORMULA
G.f.: (x^4+2*x^3+x^2+2*x+1)*(x+1)^2 / ((1-x)*(1-x^5)). - N. J. A. Sloane, Mar 28 2018
Conjecture: a(n) ~ 28*n/5. - Stefano Spezia, Mar 29 2023
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 5, 11, 17, 23, 28, 33}, 100] (* Paolo Xausa, Nov 16 2023 *)
PROG
(PARI) See Links section.
CROSSREFS
Cf. A301716.
Coordination sequences for the 20 2-uniform tilings in the order in which they appear in the Galebach catalog, together with their names in the RCSR database (two sequences per tiling): #1 krt A265035, A265036; #2 cph A301287, A301289; #3 krm A301291, A301293; #4 krl A301298, A298024; #5 krq A301299, A301301; #6 krs A301674, A301676; #7 krr A301670, A301672; #8 krk A301291, A301293; #9 krn A301678, A301680; #10 krg A301682, A301684; #11 bew A008574, A296910; #12 krh A301686, A301688; #13 krf A301690, A301692; #14 krd A301694, A219529; #15 krc A301708, A301710; #16 usm A301712, A301714; #17 krj A219529, A301697; #18 kre A301716, A301718; #19 krb A301720, A301722; #20 kra A301724, A301726.
Sequence in context: A314235 A314236 A314237 * A314238 A314239 A314240
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2018
EXTENSIONS
More terms from Rémy Sigrist, Mar 28 2018
STATUS
approved

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Last modified July 13 04:46 EDT 2024. Contains 374267 sequences. (Running on oeis4.)