A067895 Write 2^n, 2^n+1, 2^n+2, ..., 2^(n+1)-1 in binary and add as if they were decimal numbers.

1, 21, 422, 8444, 168888, 3377776, 67555552, 1351111104, 27022222208, 540444444416, 10808888888832, 216177777777664, 4323555555555328, 86471111111110656, 1729422222222221312, 34588444444444442624, 691768888888888885248, 13835377777777777770496, 276707555555555555540992

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (22,-40).

Formula

G.f.: (1 - x)/(1 - 22x + 40*x^2).

a(n) = 2^(n-1)*(19*10^n - 1)/9.

a(n) = 22*a(n-1) - 40*a(n-2).

E.g.f.: exp(2*x)*(19*exp(18*x) - 1)/18. - Stefano Spezia, Apr 03 2023

Example

2^2 to 2^3-1 = 4 through 7 = 100, 101, 110 and 111 in binary and when summed = 422.

Mathematica

Table[Total[FromDigits[IntegerDigits[#, 2]]&/@(Range[2^n, 2^(n+1)-1])], {n, 0, 20}] Harvey P. Dale, May 20 2012

Prog

(PARI) a(n)=if(n<0, 0, 2^(n-1)*(19*10^n-1)/9)

Crossrefs

Cf. A067894.

Sequence in context: A170740 A064108 A353144 * A215856 A297692 A218840

Adjacent sequences: A067892 A067893 A067894 * A067896 A067897 A067898

Keyword

nonn,base,easy

Author

N. J. A. Sloane, May 15 2003

Status

approved