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A301620 a(n) is the total number of top arches with exactly one covering arch for semi-meanders with n top arches. 2
0, 0, 2, 4, 18, 42, 156, 398, 1398, 3778, 12982, 36522, 124290, 360182, 1220440, 3618090, 12237698, 36938158, 124880222, 382471606, 1293363816, 4009185912, 13565790984, 42478788432, 143851766298, 454339269482, 1539997455570, 4900091676662, 16624834778474, 53240459608298 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n>2, a(n-2) is the number of ways to fold a strip of n stamps with leaf 1 on top and the n leaf not adjacent to the n-1 leaf. Example n = 6, a(6-2) = 4: 125436, 126345, 154362, 163452. - Roger Ford, Mar 29 2019

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n) = A000682(n+2) - 2*A000682(n+1).

a(n) = Sum_{k=3..floor((n+3)/2)} (A259689(n+1,k)*(k-2)). - Roger Ford, Dec 10 2018

a(n) = 2*A259702(n+2). - Roger Ford, Dec 24 2018

EXAMPLE

For n = 4, a(4) = 4.  + + are underneath the starting and ending of each arch with exactly one covering arch.

          /\                  /\

         //\\         /\     //\\       /\

      /\///\\\,  /\/\//\\,  ///\\\/\,  //\\/\/\ .

         +  +         ++     +  +       ++

MATHEMATICA

A000682 = Import["https://oeis.org/A000682/b000682.txt", "Table"][[All, 2]];

a[n_] := A000682[[n + 2]] - 2*A000682[[n + 1]];

Array[a, 30] (* Jean-Fran├žois Alcover, Sep 02 2019 *)

CROSSREFS

Cf. A000682, A259689.

Sequence in context: A063101 A143533 A064723 * A240316 A151449 A045664

Adjacent sequences:  A301617 A301618 A301619 * A301621 A301622 A301623

KEYWORD

nonn

AUTHOR

Roger Ford, Mar 24 2018

STATUS

approved

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Last modified January 22 13:41 EST 2020. Contains 331149 sequences. (Running on oeis4.)