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A182173
Number of inequivalent expressions involving n operands.
3
2, 10, 94, 1466, 31814, 887650, 30259198, 1218864842, 56644903958, 2983300619410, 175598066553166, 11423394497044154, 813897286250604326, 63030237104398839490, 5271647928235911880222, 473558482553909252128298, 45473767604938843870986422, 4648336478135316689480390770
OFFSET
1,1
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.
Jingzhe Tang, Table of n, a(n) for n = 1..300 (first 90 terms from David Radcliffe)
Ruud H.G. van Tol, Corrected Python script
Wikipedia, 24 Game
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
Cf. A140606.
Sequence in context: A100622 A355782 A103436 * A362643 A160940 A346649
KEYWORD
nonn
AUTHOR