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 A068018 #20 Aug 18 2024 23:03:40
%S A068018 0,1,2,4,6,12,18,40,62,148,234,576,918,2284,3650,9112,14574,36420,
%T A068018 58266,145648,233030,582556,932082,2330184,3728286,9320692,14913098,
%U A068018 37282720,59652342,149130828,238609314,596523256,954437198,2386092964,3817748730,9544371792
%N A068018 Number of fixed points in all 132- and 213-avoiding permutations of {1,2,...,n} (these are permutations with runs consisting of consecutive integers).
%H A068018 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-8,4).
%F A068018 a(n) = 2^n/4 - (-2)^n/36 + 2*n/3 - 2/9.
%F A068018 G.f.: z*(1 - 3*z^2)/((1 - 4*z^2)*(1 - z)^2).
%F A068018 E.g.f.: (cosh(x)*(5*sinh(x) + 6*x - 2) + 2*(cosh(2*x) + (3*x - 1)*sinh(x)))/9. - _Stefano Spezia_, Jun 12 2023
%e A068018 a(3) = 4 because the permutations 123, 231, 312, 321 of {1,2,3} contain 4 fixed points altogether (all three entries of the first permutation and entry 2 in the last one).
%p A068018 seq(2^n/4-(-2)^n/36+2*n/3-2/9,n=0..40);
%Y A068018 Cf. A061547.
%K A068018 nonn,easy
%O A068018 0,3
%A A068018 _Emeric Deutsch_, Mar 22 2002