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A301670
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Coordination sequence for node of type V1 in "krr" 2-D tiling (or net).
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38
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1, 4, 8, 12, 16, 22, 26, 26, 36, 36, 44, 42, 54, 50, 64, 56, 72, 66, 82, 70, 92, 80, 100, 86, 110, 94, 120, 100, 128, 110, 138, 114, 148, 124, 156, 130, 166, 138, 176, 144, 184, 154, 194, 158, 204, 168, 212, 174, 222, 182, 232, 188, 240, 198, 250, 202, 260
(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, bottom row, 1st tiling.
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LINKS
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FORMULA
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Based on the b-file, the g.f. appears to be
(-2*x^9+x^8+5*x^7+16*x^6+21*x^5+22*x^4+19*x^3+12*x^2+5*x+1) / ((1+x)*(1-x^3)*(1-x^4)). - N. J. A. Sloane, Mar 25 2018
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MATHEMATICA
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LinearRecurrence[{-1, 0, 1, 2, 1, 0, -1, -1}, {1, 4, 8, 12, 16, 22, 26, 26, 36, 36}, 100] (* Paolo Xausa, Nov 15 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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