A131568 a(n) = sum of numbers which in base 2 contain exactly n digits 1 and not more than n digits 0.

0, 3, 45, 630, 8925, 128898, 1891890, 28113228, 421717725, 6372696330, 96865261350, 1479397776948, 22684103302770, 348986220258900, 5384358887026500, 83278084352019480, 1290810308357922525, 20045524792117559130, 311819274557663622750, 4857816066846093281700

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..832

Formula

a(n) = (2*n)!*(2^(2*n)-1)/(2*n!*n!). [Corrected by Michel Marcus, Aug 22 2022]

From Peter Luschny, Aug 22 2022: (Start)

a(n) = (4^n - 1)*binomial(2*n, n) / 2.

a(n) = [x^n] ((1 - 16*x)^(-1/2) - (1 - 4*x)^(-1/2)) / 2. (End)

Example

For n=2, we have these integers in base 2: 11, 101, 110, 1001, 1010, and 1100; so a(2) = 3+5+6+9+10+12 = 45.

Mathematica

Array[(4^# - 1)*Binomial[2 #, #]/2 &, 20, 0] (* Michael De Vlieger, Aug 22 2022 *)

Crossrefs

Sequence in context: A270064 A141445 A076140 * A287031 A124487 A266698

Adjacent sequences: A131565 A131566 A131567 * A131569 A131570 A131571

Keyword

nonn,base,easy

Author

Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 27 2007

Extensions

More terms from Peter Luschny, Aug 22 2022

Status

approved