OFFSET
1,3
COMMENTS
For n>2, a(n-2) is the number of ways to fold a strip of n stamps with leaf 1 on top and the n leaf not adjacent to the n-1 leaf. Example n = 6, a(6-2) = 4: 125436, 126345, 154362, 163452. - Roger Ford, Mar 29 2019
For n>2, a(n-2) is the number of ways to fold a strip of n stamps with leaf 1 on top and leaf 2 not in the second position and not in the n-th position. Example, for n = 6, a(6-2) = 4: 143265, 156234, 165234, 143256. - Roger Ford, Mar 12 2021
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..43
FORMULA
a(n) = Sum_{k=3..floor((n+3)/2)} (A259689(n+1,k)*(k-2)). - Roger Ford, Dec 10 2018
a(n) = 2*A259702(n+2). - Roger Ford, Dec 24 2018
EXAMPLE
For n = 4, a(4) = 4. + + are underneath the starting and ending of each arch with exactly one covering arch.
/\ /\
//\\ /\ //\\ /\
/\///\\\, /\/\//\\, ///\\\/\, //\\/\/\ .
+ + ++ + + ++
MATHEMATICA
Array[a, 30] (* Jean-François Alcover, Sep 02 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger Ford, Mar 24 2018
STATUS
approved