|
|
A214843
|
|
Number of formula representations of n using addition, exponentiation and the constant 1.
|
|
4
|
|
|
1, 1, 2, 6, 16, 48, 152, 502, 1694, 5832, 20420, 72472, 260096, 942304, 3441584, 12658128, 46842920, 174289108, 651610504, 2446686568, 9222628592, 34886505168, 132387975040, 503857644160, 1922782984688, 7355686851696, 28203617340756, 108368274550664
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 1: 1.
a(2) = 1: 11+.
a(3) = 2: 111++, 11+1+.
a(4) = 6: 1111+++, 111+1++, 11+11++, 111++1+, 11+1+1+, 11+11+^.
a(5) = 16: 11111++++, 1111+1+++, 111+11+++, 1111++1++, 111+1+1++, 111+11+^+, 11+111+++, 11+11+1++, 111++11++, 11+1+11++, 1111+++1+, 111+1++1+, 11+11++1+, 111++1+1+, 11+1+1+1+, 11+11+^1+.
All formulas are given in postfix (reverse Polish) notation but other notations would give the same results.
|
|
MAPLE
|
with(numtheory):
a:= proc(n) option remember; `if`(n=1, 1,
add(a(i)*a(n-i), i=1..n-1)+
add(a(root(n, p))*a(p), p=divisors(igcd(seq(i[2],
i=ifactors(n)[2]))) minus {0, 1}))
end:
seq(a(n), n=1..40);
|
|
MATHEMATICA
|
a[1] = 1; a[n_] := a[n] = Sum[a[i]*a[n-i], {i, 1, n-1}] + Sum[a[n^(1/p)] * a[p], {p, Divisors[GCD @@ FactorInteger[n][[All, 2]]] ~Complement~ {0, 1} } ];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|