A056189 a(n) = 2^n - A056188(n).

1, 2, 2, 8, 2, 52, 2, 128, 170, 764, 2, 2488, 2, 11624, 16928, 32768, 2, 181324, 2, 555296, 931610, 2802584, 2, 11007664, 6643782, 43955032, 44739242, 136585808, 2, 720895864, 2, 2147483648, 3250384970, 10923540812, 11517062218

Offset

1,2

Comments

For n > 1, a(n) is the number of binary words of length n such that the numbers of 0's and 1's are not coprime. - Bartlomiej Pawlik, Sep 03 2023

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = 2^n-Sum{binomial[n, k]; k>0, GCD[n, k]=1}, for n>1.

a(n) = 2 for primes.

Example

For n=6, a(6)=52 because the sum of coefficients is restricted only to k=1,5 so a(6)=64-6-6.

Prog

(PARI) a(n) = if (n==1, 1, 2^n - sum(k=0, n, if (gcd(n, k) == 1, binomial(n, k)))); \\ Michel Marcus, Mar 22 2020

Crossrefs

Cf. A056045, A056188.

Sequence in context: A095997 A274139 A283995 * A331639 A079242 A121860

Adjacent sequences: A056186 A056187 A056188 * A056190 A056191 A056192

Keyword

nonn

Author

Labos Elemer, Aug 02 2000

Status

approved