A276051 - OEIS

%I #11 Dec 07 2018 04:56:40

%S 1,2,4,10,28,80,244,732,2320,7172,23212,73228,240184,768932,2545568,

%T 8240604,27468352,89699652,300579836,988463844

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

%F Conjectured formula for n>=3.

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

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

%F Example:      /\     r(x)=3

%F          /\/\//\\

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

%F Example:      /\

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

%F 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

%F                                                 /\(/\)//\\

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

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

%e a(4)=10       /\       /\      /\          /\

%e          /\/\//\\     //\\    //\\/\/\    //\\

%e                    /\///\\\              ///\\\/\.

%Y Cf. A000682.

%K nonn,more

%O 1,2

%A _Roger Ford_, Aug 17 2016

%E a(11)-a(20) from _Andrew Howroyd_, Dec 07 2018