The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A333971 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#14 by N. J. A. Sloane at Tue Sep 08 03:25:15 EDT 2020

STATUS

proposed

approved

#13 by Omar E. Pol at Thu Sep 03 20:16:25 EDT 2020

STATUS

editing

proposed

#12 by Omar E. Pol at Thu Sep 03 20:16:11 EDT 2020

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).

STATUS

proposed

editing

#11 by Roger Ford at Thu Sep 03 19:53:37 EDT 2020

STATUS

editing

proposed

#10 by Roger Ford at Thu Sep 03 19:49:51 EDT 2020

COMMENTS

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

The number of semi-meanders in generation n (A000682(n).) that have an arch adjacent to the center with length 1 = 2*A000682(n-1).

KEYWORD

nonn,changed,more

STATUS

proposed

editing

Discussion

Thu Sep 03

19:53

Roger Ford: .) is a typo that I missed.  I reworked the comments and added more to the keywords.

#9 by Roger Ford at Thu Sep 03 13:28:26 EDT 2020

STATUS

editing

proposed

Discussion

Thu Sep 03

13:35

Omar E. Pol: Could you please gives us more terms in your proposed sequences? (3 1/2 lines in the Data section), otherwise should be added the keyword "more".

13:42

Omar E. Pol: What is ".)"?

18:11

Omar E. Pol: I think the comments needs work.

18:12

Omar E. Pol: For example: see the phrase "in generation n (A000682(n).)"

#8 by Roger Ford at Thu Sep 03 13:28:12 EDT 2020

NAME

allocated for Roger Forda(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.

DATA

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 in generation n (A000682(n).) that have a starting or ending arch of length 1 = 2*A000682(n-1).

The number of semi-meanders in generation n (A000682(n).) that have an arch adjacent to the center with length 1 = 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.

KEYWORD

allocated

nonn

AUTHOR

Roger Ford, Sep 03 2020

STATUS

approved

editing

#7 by Roger Ford at Thu Sep 03 13:28:12 EDT 2020

NAME

allocated for Roger Ford

KEYWORD

recycled

allocated

#6 by R. J. Mathar at Wed Sep 02 11:40:25 EDT 2020

STATUS

editing

approved

#5 by R. J. Mathar at Wed Sep 02 11:40:23 EDT 2020

NAME

allocated for Bryann Barbosa

KEYWORD

allocated

recycled

STATUS

approved

editing