A333971 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.

1, 2, 4, 8, 24, 56, 168, 432, 1320, 3608, 11216, 31952, 100720, 295600, 942272, 2828112, 9097256, 27785112, 90048656, 278899152, 909566560, 2849498656, 9342566152, 29548420688, 97323261664

Offset: 2

Author

Roger Ford, Sep 03 2020

Keywords

• nonn
• more

Comments

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).

Examples

			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.
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.
		

Crossrefs

Cf. A000682.

Formula

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