A133752 a(n) = 256^n.

1, 256, 65536, 16777216, 4294967296, 1099511627776, 281474976710656, 72057594037927936, 18446744073709551616, 4722366482869645213696, 1208925819614629174706176, 309485009821345068724781056

Offset

0,2

Comments

Number of different possible values that a file of n bytes can have; each byte has 8 bits and each bit can be 0 or 1.

The sequence shows how many different files can exist even with a very small amount of data (just a few bytes). With just 5 bytes of data, there are 1099511627776 different possible files.

Partial sums are in A218723. - M. F. Hasler, Nov 05 2012

Links

Table of n, a(n) for n=0..11.

Index entries for linear recurrences with constant coefficients, signature (256).

Formula

From Elmo R. Oliveira, Aug 11 2024: (Start)

G.f.: 1/(1-256*x).

E.g.f.: exp(256*x).

a(n) = 256*a(n-1), n > 0. (End)

Example

a(1) = 256^1 = 256 --> there are 256 possible 1-byte files;
a(2) = 256^2 = 65536 --> there are 65536 possible 2-byte files;
a(3) = 256^3 = 16777216 --> there are 16777216 possible 3-byte files;
a(4) = 256^4 = 4294967296 --> there are 4294967296 possible 4-byte files;
a(5) = 256^5 = 1099511627776 --> there are 1099511627776 possible 5-byte files.

Mathematica

lst={}; Do[AppendTo[lst, 256^n], {n, 0, 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 02 2009 *)
256^Range[0, 20] (* Harvey P. Dale, Aug 21 2014 *)

Prog

(Python)
def A133752(n): return 1<<(n<<3) # Chai Wah Wu, Nov 10 2022

Crossrefs

Subsequence of A000079.

Cf. A218723.

Sequence in context: A189110 A223803 A223581 * A144322 A223266 A222101

Adjacent sequences: A133749 A133750 A133751 * A133753 A133754 A133755

Keyword

easy,nonn

Author

Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jan 01 2008

Extensions

Edited by Jon E. Schoenfield, Jan 24 2015

Status

approved