OFFSET
1,1
COMMENTS
Each operand must be used exactly once, and the only allowed operations are addition, subtraction, multiplication, division, and unary minus. Parentheses are permitted. This sequence differs from A140606 by allowing unary minus.
LINKS
Jingzhe Tang, Table of n, a(n) for n = 1..300 (first 90 terms from David Radcliffe)
David Radcliffe, Python script
Ruud H.G. van Tol, Corrected Python script
Wikipedia, 24 Game
Zhujun Zhang, A Chinese web page on exponential generating function
Zhujun Zhang, A Chinese web page on approximation
FORMULA
From Zhujun Zhang, Aug 11 2018: (Start)
E.g.f: A(x) = B(x) + C(x) - 2*x, where B(x) = 2*x + exp(C(x)) - 1 - C(x) and C(x) = 2*x + 2*exp(B(x)) - 2*exp(B(x)/2) - B(x).
a(n) ~ (n/(e*b))^n * sqrt(b)*c/n where b=0.16142418303980816579438744831086877555003744810690... and c=1.8772213095052105788245813534431275116981368728916.... (End)
EXAMPLE
When n=2, there are 10 inequivalent expressions: a+b, a-b, b-a, -a-b, a*b, -a*b, a/b, -a/b, b/a, -b/a.
PROG
(PARI) {a(n) = my(A, B=x +x*O(x^n), C=x +x*O(x^n)); for(i=1, n, B = 2*x + exp(C) - 1 - C; C = 2*x + 2*exp(B) - 2*exp(B/2) - B ); A = B + C - 2*x; n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Aug 12 2018 - After formula by Zhujun Zhang
CROSSREFS
KEYWORD
nonn
AUTHOR
David Radcliffe, Apr 16 2012
STATUS
approved