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

Author

Roger Ford, Sep 08 2020

Keywords

• nonn
• more

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.

Examples

			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.

Formula

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