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 A334615 #10 Sep 22 2020 00:39:29 %S A334615 0,0,0,2,0,10,6,72,86,602,982,5426,10558,51246,111602,500076,1177210, %T A334615 5001518,12462762,51003906,132711162,528420604,1422458280,5547419160, %U A334615 15347206464 %N A334615 a(n) is the number of semi-meanders with n top arches that has no arch of length 1 at the ends of the top arch configuration and no arch of length 1 adjacent to the center of the top arch configuration. %C A334615 The number of semi-meanders with n top arches is A000682(n). If a formula for a(n) could be found without using the values for A000682(n) or A301620(n) then there would be a recursive formula for semi-meanders with n top arches. %F A334615 For n>= 4: a(n) = A301620(n) - 2*A301620(n-1) = A000682(n) - 4*A000682(n-1) + 4*A000682(n-2). %e A334615 For n = 7: a(7) = 10. 11111000001100, 11110000111000, 11110000101100, 11101000110100, 11100011110000, 11100011100100, 11011000111000, 11010011101000, 11001111100000, 11001011110000. /\ %e A334615 / \ %e A334615 / /\ \ %e A334615 11001011110000 --> /\ / //\\ \ 10 = arch length 1 %e A334615 //\\ /\ / ///\\\ \ %e A334615 end center| end %e A334615 11 01 11 00 no 10 in designated positions. %Y A334615 Cf. A000682, A301620. %K A334615 nonn,more %O A334615 2,4 %A A334615 _Roger Ford_, Sep 08 2020