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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A007333 An upper bound on the biplanar crossing number of the complete graph on n nodes.

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%I A007333 M3306 #34 Feb 13 2022 17:45:48
%S A007333 0,0,0,0,0,0,0,0,4,7,12,18,37,53,75,100,152,198,256,320,430,530,650,
%T A007333 780,980,1165,1380,1610,1939,2247,2597,2968,3472,3948,4480,5040,5772,
%U A007333 6468,7236,8040,9060,10035,11100,12210,13585,14905,16335,17820,19624,21362
%N A007333 An upper bound on the biplanar crossing number of the complete graph on n nodes.
%C A007333 This bound in based on a particular decomposition of K_n (see Owens for details). The actual biplanar crossing number for K_9 is 1 (not 4 as given by this bound). - _Sean A. Irvine_, Dec 30 2019
%D A007333 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007333 Colin Barker, <a href="/A007333/b007333.txt">Table of n, a(n) for n = 1..1000</a>
%H A007333 A. Owens, <a href="https://doi.org/10.1109/TCT.1971.1083266">On the biplanar crossing number</a>, IEEE Trans. Circuit Theory, 18 (1971), 277-280.
%H A007333 A. Owens, <a href="/A007333/a007333.pdf">On the biplanar crossing number</a>, IEEE Trans. Circuit Theory, 18 (1971), 277-280. [Annotated scanned copy]
%H A007333 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,3,-6,3,0,-3,6,-3,0,1,-2,1).
%F A007333 a(4*k) = k * (k-1) * (k-2) * (7*k-3) / 6, a(4*k+1) = k * (k-1) * (7*k^2-10*k+4) / 6, a(4*k+2) = k * (k-1) * (7*k^2-3*k-1) / 6, a(4*k+3) = k^2 * (k-1) * (7*k+4) / 6 [from Owens]. - _Sean A. Irvine_, Dec 30 2019; [typo corrected by _Colin Barker_, Feb 01 2020]
%F A007333 From _Colin Barker_, Jan 28 2020: (Start)
%F A007333 G.f.: x^9*(4 - x + 2*x^2 + x^3 + x^4) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^3).
%F A007333 a(n) = 2*a(n-1) - a(n-2) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) - 3*a(n-8) + 6*a(n-9) - 3*a(n-10) + a(n-12) - 2*a(n-13) + a(n-14) for n>14.
%F A007333 (End)
%t A007333 LinearRecurrence[{2,-1,0,3,-6,3,0,-3,6,-3,0,1,-2,1},{0,0,0,0,0,0,0,0,4,7,12,18,37,53},70] (* _Harvey P. Dale_, Feb 13 2022 *)
%o A007333 (PARI) concat([0,0,0,0,0,0,0,0], Vec(x^9*(4 - x + 2*x^2 + x^3 + x^4) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^3) + O(x^40))) \\ _Colin Barker_, Feb 02 2020
%Y A007333 Cf. A000241, A028723.
%K A007333 nonn,nice,easy
%O A007333 1,9
%A A007333 _N. J. A. Sloane_
%E A007333 More terms and title clarified by _Sean A. Irvine_, Dec 30 2019