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Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the largest region in the resulting graph occupies a(n)/2^n of the whole sheet.
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%I #7 Mar 29 2021 15:16:36

%S 1,1,2,4,7,13,26,51,97,191,366,713,1375,2673,5164,10031,19405,37663,

%T 72922,141461,274019,531405,1029640,1996395,3868793,7500411,14536342,

%U 28179521,54617039

%N Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the largest region in the resulting graph occupies a(n)/2^n of the whole sheet.

%C A342759 is the main sequence for this entry.

%C The sequence {a(n)/2^n, n >= 0} is bounded and weakly decreasing, hence it has a limit.

%H Rémy Sigrist, <a href="/A342764/a342764.png">Illustration of initial terms</a>

%H Rémy Sigrist, <a href="/A342764/a342764.txt">C# program for A342764</a>

%F a(n+1) <= 2*a(n).

%e See illustration in Links section.

%o (C#) See Links section.

%Y Cf. A342759.

%K nonn,more

%O 0,3

%A _Rémy Sigrist_, Mar 24 2021