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A301283 Coordination sequence for node of type V1 in "car" 2-D tiling (or net).

%I A301283 #15 Mar 31 2018 16:25:06
%S A301283 1,3,6,8,12,17,18,20,26,29,29,33,39,41,41,45,52,54,52,57,66,66,63,70,
%T A301283 79,78,75,82,92,91,86,94,106,103,97,107,119,115,109,119,132,128,120,
%U A301283 131,146,140,131,144,159,152,143,156,172,165,154,168,186,177,165
%N A301283 Coordination sequence for node of type V1 in "car" 2-D tiling (or net).
%H A301283 Rémy Sigrist, <a href="/A301283/b301283.txt">Table of n, a(n) for n = 0..1000</a>
%H A301283 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/car">The car tiling (or net)</a>
%H A301283 Rémy Sigrist, <a href="/A301283/a301283.gp.txt">PARI program for A301283</a>
%H A301283 Rémy Sigrist, <a href="/A301283/a301283_1.png">Illustration of first terms</a>
%F A301283 Conjectures from _Colin Barker_, Mar 30 2018: (Start)
%F A301283 G.f.: (1 + 2*x + 5*x^2 + 5*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 + x^8 - x^10) / ((1 - x)^2*(1 + x^2)^2*(1 + x + x^2)).
%F A301283 a(n) = a(n-1) - 2*a(n-2) + 3*a(n-3) - 2*a(n-4) + 3*a(n-5) - 2*a(n-6) + a(n-7) - a(n-8) for n>8.
%F A301283 (End)
%F A301283 Equivalent conjecture: 12*a(n) = 37*n+4*b(n)+6*(-1)^(n/2)*A142150(n+2)+3*c(n) for n>2, where b(n)=0,-1,1 (3-periodic, n>=0) and c(n) = -6,5,6,-5 (4-periodic, n>=0). - _R. J. Mathar_, Mar 31 2018
%o A301283 (PARI) See Links section.
%Y A301283 Cf. A301285.
%K A301283 nonn
%O A301283 0,2
%A A301283 _N. J. A. Sloane_, Mar 23 2018
%E A301283 More terms from _Rémy Sigrist_, Mar 28 2018