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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.
0
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).
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
KEYWORD
nonn,more
AUTHOR
Roger Ford, Sep 03 2020
STATUS
approved