A334615 a(n) is the number of semi-meanders with n top arches that has no arch of length 1 at the ends of the top arch configuration and no arch of length 1 adjacent to the center of the top arch configuration.

0, 0, 0, 2, 0, 10, 6, 72, 86, 602, 982, 5426, 10558, 51246, 111602, 500076, 1177210, 5001518, 12462762, 51003906, 132711162, 528420604, 1422458280, 5547419160, 15347206464

Offset

2,4

Comments

The number of semi-meanders with n top arches is A000682(n). If a formula for a(n) could be found without using the values for A000682(n) or A301620(n) then there would be a recursive formula for semi-meanders with n top arches.

Links

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

Formula

For n>= 4: a(n) = A301620(n) - 2*A301620(n-1) = A000682(n) - 4*A000682(n-1) + 4*A000682(n-2).

Example

For n = 7: a(7) = 10.  11111000001100, 11110000111000, 11110000101100, 11101000110100, 11100011110000, 11100011100100, 11011000111000, 11010011101000, 11001111100000, 11001011110000.       /\
                                       /  \
                                      / /\ \
      11001011110000 -->   /\        / //\\ \    10 = arch length 1
                          //\\  /\  / ///\\\ \
                         end   center|      end
                         11       01  11    00    no 10 in designated positions.

Crossrefs

Cf. A000682, A301620.

Sequence in context: A337056 A362994 A371551 * A303350 A351879 A070681

Adjacent sequences: A334612 A334613 A334614 * A334616 A334617 A334618

Keyword

nonn,more

Author

Roger Ford, Sep 08 2020

Status

approved