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Coordination sequence for the bil tiling (or net) with respect to a trivalent node of the fourth type.
4

%I #12 Apr 01 2018 10:49:18

%S 1,3,6,8,11,16,19,18,23,30,29,30,35,42,43,40,47,52,55,56,55,64,67,68,

%T 71,72,79,78,83,90,85,90,95,102,103,96,107,112,115,116,111,124,127,

%U 128,131,128,139,138,143,150,141,150,155,162,163,152,167,172,175,176

%N Coordination sequence for the bil tiling (or net) with respect to a trivalent node of the fourth type.

%H Rémy Sigrist, <a href="/A298795/b298795.txt">Table of n, a(n) for n = 0..1000</a>

%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/bil">The bil tiling (or net)</a>

%H Rémy Sigrist, <a href="/A298795/a298795.png">Illustration of first terms</a>

%H Rémy Sigrist, <a href="/A298795/a298795.gp.txt">PARI program for A298795</a>

%F Conjectures from _Colin Barker_, Mar 30 2018: (Start)

%F G.f.: (1 + 2*x + 5*x^2 + 6*x^3 + 11*x^4 + 12*x^5 + 15*x^6 + 12*x^7 + 19*x^8 + 12*x^9 + 15*x^10 + 12*x^11 + 11*x^12 + 8*x^13 + 5*x^14 + 2*x^15 + x^16 - x^18) / ((1 - x)^2*(1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)^2).

%F a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 3*a(n-5) - 3*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + 3*a(n-11) - 2*a(n-12) + 2*a(n-13) - 2*a(n-14) + a(n-15) - a(n-16) for n>16.

%F (End)

%o (PARI) See Links section.

%Y Cf. A298792, A298793, A298794.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 27 2018

%E More terms from _Rémy Sigrist_, Mar 30 2018