A276051 a(n) is the number of top arches with length =1 for all semi meander solutions with n top arches.

1, 2, 4, 10, 28, 80, 244, 732, 2320, 7172, 23212, 73228, 240184, 768932, 2545568, 8240604, 27468352, 89699652, 300579836, 988463844

Offset: 1

Author

Roger Ford, Aug 17 2016

Keywords

• nonn
• more

Examples

			a(4)=10       /\       /\      /\          /\
         /\/\//\\     //\\    //\\/\/\    //\\
                   /\///\\\              ///\\\/\.
		

Crossrefs

Cf. A000682.

Formula

Conjectured formula for n>=3.

M(n)= number of semi meanders solutions for n top arches. A000682.

r(x)= number of top arches with no covering arch for solution x of M(n).

Example: /\ r(x)=3

/\/\//\\

h(x)= number of top arches with length =1 for solution x of M(n).

Example: /\

/\/\//\\ h(x)=3

i(x)= number of uncovered top arches with length =1 and in an internal position for solution x of M(n). Example:() /\ i(x)=1

/\(/\)//\\

a(n+1)= sum of x=1 to M(n)for [r(x)*h(x)-i(x)] + 2*M(n)-2*M(n-1)

a(5)=(3*3-1)+(3*3-1)+(2*2-0)+(2*2-0)+2*4-2*2= 28.

Extensions

a(11)-a(20) from Andrew Howroyd, Dec 07 2018