

A301710


Coordination sequence for node of type V2 in "krc" 2D tiling (or net).


38



1, 5, 11, 17, 22, 27, 33, 39, 44, 49, 55, 61, 66, 71, 77, 83, 88, 93, 99, 105, 110, 115, 121, 127, 132, 137, 143, 149, 154, 159, 165, 171, 176, 181, 187, 193, 198, 203, 209, 215, 220, 225, 231, 237, 242, 247, 253, 259, 264, 269, 275, 281, 286, 291, 297, 303
(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, 1st tiling.


LINKS



FORMULA

G.f.: (x^4+3*x^3+3*x^2+3*x+1)/((x^2+1)*(x1)^2); for n>0, a(2*t)=11*t, a(4*t+1)=22*t+5, a(4*t+3)=22*t+17. These should be easy to prove by the coloring book method (see link).
a(n) = ((i)^(1+n) + i^(1+n) + 22*n) / 4 for n>0, where i=sqrt(1) (conjectured).  Colin Barker, Apr 07 2018


MATHEMATICA

LinearRecurrence[{2, 2, 2, 1}, {1, 5, 11, 17, 22}, 100] (* Paolo Xausa, Nov 14 2023 *)


PROG

(PARI) See Links section.


CROSSREFS

Coordination sequences for the 20 2uniform 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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



