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<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 2, 2, 0, -1, -1).
LinearRecurrence[{-1, 0, 2, 2, 0, -1, -1}, {1, 4, 8, 14, 16, 26, 22, 34, 36}, 100] (* Paolo Xausa, Nov 15 2023 *)
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Linear recurrence and g.f. confirmed by Shutov/Maleev link. - Ray Chandler, Aug 31 2023
Anton Shutov and Andrey Maleev, <a href="https://doi.org/10.1515/zkri-2020-0002">Coordination sequences of 2-uniform graphs</a>, Z. Kristallogr., 235 (2020), 157-166. See supplementary material, krb, vertex u_1.
<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, 2, 2, 0, -1, -1).
Conjectures: (a) G.f. = -(2*x^8-x^7-5*x^6-18*x^5-20*x^4-20*x^3-12*x^2-5*x-1)/((x+1)*(x-1)^2*(x^2+x+1)^2). (b) Satisfies the recurrence {( - 2*n^5 - 13*n^4 - 22*n^3 + 7*n^2 + 30*n)*a(n) + ( - 2*n^5 - 13*n^4 - 25*n^3 + n^2 + 39*n)*a(n + 1) + ( - 6*n^2 + 6*n)*a(n + 2) + (2*n^5 + 7*n^4 + 7*n^3 - 7*n^2 - 9*n)*a(n + 3) + (2*n^5 + 7*n^4 + 4*n^3 - 7*n^2 - 6*n)*a(n + 4) = 0, a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 14, a(4) = 16, a(5) = 26}. - N. J. A. Sloane, Mar 28 2018
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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, A361684A301684; #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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Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
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Equivalent conjecture: 9*a(n) = 40*n -18*(-1)^n -6*(-1)^n*A076118(n+1) +6*A049347(n) -4*A049347(n-1). - R. J. Mathar, Apr 01 2018
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