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A301710
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Coordination sequence for node of type V2 in "krc" 2-D tiling (or net).
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38
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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)
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OFFSET
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0,2
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COMMENTS
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Linear recurrence and g.f. confirmed by Shutov/Maleev link. - Ray Chandler, Aug 30 2023
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: (x^4+3*x^3+3*x^2+3*x+1)/((x^2+1)*(x-1)^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
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MATHEMATICA
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LinearRecurrence[{2, -2, 2, -1}, {1, 5, 11, 17, 22}, 100] (* Paolo Xausa, Nov 14 2023 *)
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PROG
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(PARI) See Links section.
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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