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

2,2

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).

Links

Table of n, a(n) for n=2..26.

Formula

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

Example

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.

Sequence in context: A291405 A306420 A361726 * A231721 A114900 A264570

Adjacent sequences: A333968 A333969 A333970 * A333972 A333973 A333974

Keyword

nonn,more

Author

Roger Ford, Sep 03 2020

Status

approved