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.
%I A047051 #22 Apr 14 2019 12:52:17
%S A047051 1,2,4,10,29,98,372,1538,6755,30996,146982,715120,3552254,17951322,
%T A047051 92045058,477882876,2508122859,13289437362,71010166670,382291606570,
%U A047051 2072025828101,11298920776704,61954857579594,341427364138880
%N A047051 Prime alternating tangle types (of knots) with n crossings.
%C A047051 G.f. is related to the classes of 2- and 3-connected planar maps with n edges. Further terms are known.
%D A047051 C. Sundberg and M. Thistlethwaite, The rate of growth of the number of prime alternating links and tangles, Pacif. J. Math., 182, No 2 (1998), 329-358.
%H A047051 Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007, <a href="/A047051/b047051.txt">Table of n, a(n) for n = 1..50</a>
%H A047051 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Knots, links and tangles</a>
%H A047051 S. R. Finch, <a href="/A002863/a002863_4.pdf">Knots, links and tangles</a>, Aug 08 2003. [Cached copy, with permission of the author]
%H A047051 C. Sundberg and M. Thistlethwaite, <a href="http://msp.berkeley.edu/pjm/1998/182-2/p06.xhtml">The rate of growth of the number of prime alternating links and tangles</a>, Pacif. J. Math., 182, No 2 (1998), 329-358.
%H A047051 P. Zinn-Justin and J.-B. Zuber, <a href="http://arXiv.org/abs/math-ph/0303049">Matrix integrals and the generation and counting of virtual tangles and links</a>, p. 12.
%H A047051 P. Zinn-Justin, <a href="http://arXiv.org/abs/math-ph/0106005">The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links</a>
%t A047051 max = 24; Clear[a, eq, s]; gf = Sum[a[k]*x^k, {k, 0, max}]; a[0] = 0; a[1] = 1; a[2] = 2; coes = CoefficientList[(x^4 - 2*x^3 + x^2)*gf^5 + (8*x^4 - 14*x^3 + 8*x^2 - 2*x)*gf^4 + (25*x^4 - 16*x^3 - 14*x^2 + 8*x + 1)*gf^3 + (38*x^4 + 15*x^3 - 30*x^2 - x + 2)*gf^2 + (28*x^4 + 36*x^3 - 5*x^2 - 12*x + 1)*gf + 8*x^4 + 17*x^3 + 8*x^2 - x, x]; eq[n_] := eq[n] = If[n == 1, Thread[Drop[coes, 3] == 0], eq[n-1] /. s[n-1] // First]; s[n_] := s[n] = (Print["n = ", n]; Solve[eq[n][[n]], a[n+2]]); sol = Table[s[n], {n, 1, max-2}] // Flatten; Table[a[n], {n, 1, max}] /. sol (* _Jean-François Alcover_, Apr 15 2014 *)
%Y A047051 Cf. A002864, A000139, A000287.
%K A047051 easy,nice,nonn
%O A047051 1,2
%A A047051 _Valery A. Liskovets_
%E A047051 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007