A333971 - OEIS

%I #14 Sep 08 2020 03:25:15

%S 1,2,4,8,24,56,168,432,1320,3608,11216,31952,100720,295600,942272,

%T 2828112,9097256,27785112,90048656,278899152,909566560,2849498656,

%U 9342566152,29548420688,97323261664

%N a(n) is the number of semi-meanders with n top arches that have at least one arch with length 1 adjacent to the center of the top arch configuration or at either end of the arch configuration.

%C The number of semi-meanders with n top arches is A000682(n). The number of semi-meanders with n top arches that have a starting or ending arch of length 1 is 2*A000682(n-1). The number of semi-meanders with n top arches that have an arch adjacent to the center with length 1 is 2*A000682(n-1).

%F For n >= 4: a(n) = 4*(A000682(n-1) - A000682(n-2)).

%e For n = 6: (10) is an arch of length 1 that is at either end of the top arch configuration or adjacent to the center of the top arch configuration, a(6) = 24.

%e 1111(10)0000(10), 111100(10)00(10), 1111000010(10), 1110(10)0100(10), 1110(10)001100, 111001(10)00(10), 1110001100(10), 111000(10)1100, 1101(10)0010(10), 110110(10)10(10), 110011(10)00(10), 110011(10)00(10), 1100(10)111000, 1100(10)1100(10), (10)1111(10)0000, (10)11(10)110000, (10)11(10)011000, (10)11(10)001100, (10)1101(10)1000, (10)1100111000, (10)1100(10)1100, (10)1011110000, (10)1011(10)0100, (10)10(10)110100.

%Y Cf. A000682.

%K nonn,more

%O 2,2

%A _Roger Ford_, Sep 03 2020