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A260785
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Leading diagonal of triangle in A259689: a(n)= number of permutations without overlaps that generate exactly 2 permutations without overlaps in a(n+1).
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2
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1, 2, 2, 6, 10, 32, 68, 220, 528, 1724, 4460, 14664, 39908, 131944, 372448, 1237016, 3589384, 11967140, 35479312, 118675768, 357957984, 1200724776, 3673173656, 12351611656, 38232022416
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OFFSET
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2,2
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COMMENTS
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a(n)= Number of semi-meander solutions for n with 2 returns to the x axis (or number of 2 distinct arch groups).
Example: n=5 -= return to x axis
/\ /\ /\
//\\ / \ /\ //\\
///\\\ / /\\ /\ //\\ ///\\\
/\-////\\\\- /\-//\//\\\- //\\-///\\\- ////\\\\-/\-
/\
/ \ /\
//\ \ //\\ /\
///\\/\\-/\- ///\\\-//\\- a(5)=6.
a(n)= Number of hills (arches with a peak at 1 and no covering arches) for semi-meander solutions with n-1 arches.
Example: n=5 semi-meander solutions with 4 arches (/\)= hill
/\ /\
/\ /\ //\\ //\\
(/\)(/\)//\\ //\\(/\)(/\) ///\\\(/\) (/\)///\\\ a(5)=6.
(End)
a(n)= Number of solutions for folding a strip of n stamps with stamp 1 on top and each solution ordering having the absolute value of the difference of the stamp number before and after stamp n equal to 1. (If stamp n is the last stamp in the solution ordering then add a(1) to the end of the ordering.)
Example: n=5
12354 |3-4| = 1, 14325(1) |2-1| = 1, 12453 |4-3| = 1,
14532 |4-3| = 1, 15234 |1-2| = 1, 13542 |3-4| = 1, a(5)=6.
(End)
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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