# Alex Gentul Homework 15 OK to share

info1:=proc() print(`An(integer n); MaxDev(real number a,positive integer <=2 d,list  w,positive integer N)`); end:
info1();


	# (1) #

	# An(integer n) computes the number of up down permutations of {1...n}

An:=proc(n) option remember;
local i,a;
if n=0 or n=1 or n=2 then
	return 1;
else
	a:=0;
	for i from 1 to n/2 do
		a:=a+binomial(n-1,2*i-1)*An(2*i-1)*An(n-2*i);
	end;
end;
a;
end:

	# (An(200)/200!)/(An(199)/199!) gets pretty close to 2/pi

	
	# (2) #

	# MaxDev(real number a,positive integer <=2 d,list w,positive integer N)

MaxDev:=proc(a,d,w,N) local P,b,i,j,w1;

Digits:=50*N*d^(nops(w));
P:=RtoS(evalf(a),d,N*d^(nops(w)));
b:=0;

	for i from 1 to nops(P)-nops(w)+1 do
		w1:=[seq(P[i+j],j=0..nops(w)-1)];
		if w1=w then
 			b:=b+1;
		end;
	end;
b;
end:


	# (3) #

	# J(n)

J:=proc(n)