Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Sep 22 2020 00:39:29
%S 0,0,0,2,0,10,6,72,86,602,982,5426,10558,51246,111602,500076,1177210,
%T 5001518,12462762,51003906,132711162,528420604,1422458280,5547419160,
%U 15347206464
%N 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 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 For n>= 4: a(n) = A301620(n) - 2*A301620(n-1) = A000682(n) - 4*A000682(n-1) + 4*A000682(n-2).
%e For n = 7: a(7) = 10. 11111000001100, 11110000111000, 11110000101100, 11101000110100, 11100011110000, 11100011100100, 11011000111000, 11010011101000, 11001111100000, 11001011110000. /\
%e / \
%e / /\ \
%e 11001011110000 --> /\ / //\\ \ 10 = arch length 1
%e //\\ /\ / ///\\\ \
%e end center| end
%e 11 01 11 00 no 10 in designated positions.
%Y Cf. A000682, A301620.
%K nonn,more
%O 2,4
%A _Roger Ford_, Sep 08 2020