

A110837


Number of ways to fold a strip of n stamps taking account of order and direction of folds.


1



1, 2, 8, 36, 176, 864, 4304, 21448, 107168, 535488, 2677088, 13383712, 66916832, 334575552, 1672869152, 8364302864, 41821471424, 209107142784, 1045535499584, 5227676426944, 26138381063744, 130691899964544, 653459494468544, 3267297445575296, 16336487201109056
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS



FORMULA

a(n) = 2 * Sum_{0<k<n} max{a(k), a(nk)} starting with a(1)=1.
a(n) ~ 0.054816154756...*5^n.


EXAMPLE

a(3) = 8 since with an initial strip of three stamps there are two possible folding positions for the initial fold, each of which could be folded up or down, so there are four possible initial folds, each leaving one possible folding position which can be folded up or down, making eight possible folding patterns.


MAPLE

a:= proc(n) option remember; `if`(n=1, 1,
2*add(max(a(k), a(nk)), k=1..n1))
end:


MATHEMATICA

a[n_] := a[n] = If[n==1, 1, 2*Sum[Max[a[k], a[nk]], {k, 1, n1}]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



