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A301299
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Coordination sequence for node of type V1 in "krq" 2-D tiling (or net).
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38
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1, 4, 8, 13, 18, 22, 26, 29, 34, 40, 44, 48, 50, 55, 62, 66, 70, 71, 76, 84, 88, 92, 92, 97, 106, 110, 114, 113, 118, 128, 132, 136, 134, 139, 150, 154, 158, 155, 160, 172, 176, 180, 176, 181, 194, 198, 202, 197, 202, 216, 220, 224, 218, 223, 238, 242, 246, 239, 244, 260, 264, 268, 260, 265, 282
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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 31 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, bottom row, 2nd tiling.
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LINKS
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A. V. Maleev, A. A. Mokrova, and A. V. Shutov, Coordination sequences of the 2-uniform graphs (Russian), Algebra, number theory and discrete geometry: modern problems and application of past problems (2019), Proceedings of the XVI International Conference in honor of the 80th birthday of Professor Michel Deza, 262-266.
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^10-4*x^9-8*x^8-13*x^7-18*x^6-20*x^5-18*x^4-13*x^3-8*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, 8, 13, 18, 22, 26, 29, 34, 40, 44}, 100] (* Paolo Xausa, Nov 15 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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