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A276051
a(n) is the number of top arches with length =1 for all semi meander solutions with n top arches.
0
1, 2, 4, 10, 28, 80, 244, 732, 2320, 7172, 23212, 73228, 240184, 768932, 2545568, 8240604, 27468352, 89699652, 300579836, 988463844
OFFSET
1,2
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.
EXAMPLE
a(4)=10 /\ /\ /\ /\
/\/\//\\ //\\ //\\/\/\ //\\
/\///\\\ ///\\\/\.
CROSSREFS
Cf. A000682.
Sequence in context: A148109 A099216 A149819 * A149820 A149821 A149822
KEYWORD
nonn,more
AUTHOR
Roger Ford, Aug 17 2016
EXTENSIONS
a(11)-a(20) from Andrew Howroyd, Dec 07 2018
STATUS
approved