|
|
A082481
|
|
Number of 1's in binary representation of C(2n,n).
|
|
1
|
|
|
1, 1, 2, 2, 3, 6, 6, 6, 6, 11, 9, 9, 9, 13, 10, 16, 14, 10, 16, 20, 14, 20, 16, 29, 26, 24, 22, 30, 24, 20, 25, 25, 30, 29, 33, 37, 35, 40, 35, 39, 37, 40, 42, 43, 36, 44, 46, 48, 48, 41, 43, 46, 50, 58, 51, 52, 52, 50, 53, 56, 54, 48, 59, 60, 57, 64, 61, 61, 64, 66, 64, 72, 73
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
Should be asymptotic to n.
|
|
MAPLE
|
seq(convert(convert(binomial(2*n, n), base, 2), `+`), n=0..100); # Robert Israel, Mar 27 2018
|
|
MATHEMATICA
|
Table[DigitCount[Binomial[2n, n], 2, 1], {n, 0, 90}] (* Harvey P. Dale, Jul 20 2023 *)
|
|
PROG
|
(PARI) a(n)=sum(k=1, length(binary(binomial(2*n, n))), component(binary(binomial(2*n, n)), k))
(PARI) a(n) = hammingweight(binomial(2*n, n)); \\ Michel Marcus, Mar 27 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|