|
|
A029930
|
|
If 2n = Sum 2^e_i, a(n) = Product 2^e_i.
|
|
7
|
|
|
1, 2, 4, 8, 8, 16, 32, 64, 16, 32, 64, 128, 128, 256, 512, 1024, 32, 64, 128, 256, 256, 512, 1024, 2048, 512, 1024, 2048, 4096, 4096, 8192, 16384, 32768, 64, 128, 256, 512, 512, 1024, 2048, 4096, 1024, 2048, 4096, 8192, 8192, 16384, 32768, 65536, 2048
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Prod_{k>=0} 1+2^(k+1)x^2^k.
a(0) = 1, a(2n) = 2^e1(n)*a(n), a(2n+1) = 2a(2n), where e1(n) = A000120(n).
|
|
EXAMPLE
|
14 = 8+4+2 so a(7) = 8*4*2 = 64.
|
|
MAPLE
|
HammingWeight := n -> add(i, i = convert(n, base, 2)):
a := proc(n) option remember; `if`(n = 0, 1,
ifelse(n::even, 2^HammingWeight(n/2)*a(n/2), 2*a(n-1))) end:
|
|
MATHEMATICA
|
e1[n_] := Total[IntegerDigits[n, 2]]; a[0] = 1; a[n_] := a[n] = If[EvenQ[ n], 2^e1[n/2] a[n/2], 2 a[n-1]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Mar 07 2016 *)
|
|
PROG
|
(PARI) a(n) = {my(bd = Vecrev(binary(n))); prod(k=1, #bd, if (bd[k], 2^k, 1)); } \\ Michel Marcus, Mar 07 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|