A133752 - OEIS

%I #32 Aug 13 2024 09:11:11

%S 1,256,65536,16777216,4294967296,1099511627776,281474976710656,

%T 72057594037927936,18446744073709551616,4722366482869645213696,

%U 1208925819614629174706176,309485009821345068724781056

%N a(n) = 256^n.

%C 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.

%C 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.

%C Partial sums are in A218723. - _M. F. Hasler_, Nov 05 2012

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (256).

%F From _Elmo R. Oliveira_, Aug 11 2024: (Start)

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

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

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

%e a(1) = 256^1 = 256 --> there are 256 possible 1-byte files;

%e a(2) = 256^2 = 65536 --> there are 65536 possible 2-byte files;

%e a(3) = 256^3 = 16777216 --> there are 16777216 possible 3-byte files;

%e a(4) = 256^4 = 4294967296 --> there are 4294967296 possible 4-byte files;

%e a(5) = 256^5 = 1099511627776 --> there are 1099511627776 possible 5-byte files.

%t lst={};Do[AppendTo[lst,256^n],{n,0,4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009 *)

%t 256^Range[0,20] (* _Harvey P. Dale_, Aug 21 2014 *)

%o (Python)

%o def A133752(n): return 1<<(n<<3) # _Chai Wah Wu_, Nov 10 2022

%Y Subsequence of A000079.

%Y Cf. A218723.

%K easy,nonn

%O 0,2

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

%E Edited by _Jon E. Schoenfield_, Jan 24 2015