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 A336398 #5 Jul 20 2020 10:56:25 %S A336398 0,2,1,4,5,14,21,48,85,182,341,704,1365,2774,5461,11008,21845,43862, %T A336398 87381,175104,349525,699734,1398101,2797568,5592405,11187542,22369621, %U A336398 44744704,89478485,178967894,357913941,715849728 %N A336398 Number of rational knots (or two-bridge knots) with n crossings (chiral pairs counted as distinct). %H A336398 C. Ernst and D. W. Sumners, <a href="https://doi.org/10.1017/S0305004100067323">The Growth of the Number of Prime Knots</a>, Math. Proc. Cambridge Philos. Soc. 102, 303-315, 1987 (see Theorem 1, formulas for TK_n^*). %H A336398 Taizo Kanenobu and Toshio Sumi, <a href="https://doi.org/10.1090/S0025-5718-1993-1176711-4">Polynomial Invariants of 2-Bridge Knots through 22 Crossings</a>, Math. Comp. 60 (1993), 771-778, S17 (see Table 2). %H A336398 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1,0,-2,-4). %F A336398 (2^(n-2) - 1) / 3 if n is even, %F A336398 (2^(n-2) + 2^((n-1)/2)) / 3 if n = 1 (mod 4), %F A336398 (2^(n-2) + 2^((n-1)/2) + 2) / 3 if n = 3 (mod 4). %F A336398 a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-5) - 4*a(n-6). %o A336398 (Python) [(2**(n-2) + [-1, 2**(n//2), -1, 2**(n//2)+2][n%4])//3 for n in range(2, 30)] %Y A336398 Cf. A018240, A090597, A329908. %K A336398 nonn,easy %O A336398 2,2 %A A336398 _Andrey Zabolotskiy_, Jul 20 2020