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A301692
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Coordination sequence for node of type V2 in "krf" 2-D tiling (or net).
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38
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1, 4, 7, 9, 12, 16, 21, 25, 26, 29, 34, 38, 41, 42, 46, 52, 55, 57, 58, 63, 70, 72, 73, 74, 80, 88, 89, 89, 90, 97, 106, 106, 105, 106, 114, 124, 123, 121, 122, 131, 142, 140, 137, 138, 148, 160, 157, 153, 154, 165, 178, 174, 169, 170, 182, 196, 191, 185, 186, 199, 214, 208, 201, 202, 216, 232, 225
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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 66, 2nd row, 1st tiling.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
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FORMULA
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G.f.: -(x^13+2*x^12-3*x^10-5*x^9-8*x^8-11*x^7-13*x^6-14*x^5-12*x^4-9*x^3-7*x^2-4*x-1)/(x^10-2*x^5+1). - N. J. A. Sloane, Mar 29 2018
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 4, 7, 9, 12, 16, 21, 25, 26, 29, 34, 38, 41, 42}, 100] (* Paolo Xausa, Nov 16 2023 *)
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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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