cp's OEIS Frontend

A133752 a(n) = 256^n.

%I A133752 #32 Aug 13 2024 09:11:11
%S A133752 1,256,65536,16777216,4294967296,1099511627776,281474976710656,
%T A133752 72057594037927936,18446744073709551616,4722366482869645213696,
%U A133752 1208925819614629174706176,309485009821345068724781056
%N A133752 a(n) = 256^n.
%C A133752 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 A133752 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 A133752 Partial sums are in A218723. - _M. F. Hasler_, Nov 05 2012
%H A133752 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (256).
%F A133752 From _Elmo R. Oliveira_, Aug 11 2024: (Start)
%F A133752 G.f.: 1/(1-256*x).
%F A133752 E.g.f.: exp(256*x).
%F A133752 a(n) = 256*a(n-1), n > 0. (End)
%e A133752 a(1) = 256^1 = 256 --> there are 256 possible 1-byte files;
%e A133752 a(2) = 256^2 = 65536 --> there are 65536 possible 2-byte files;
%e A133752 a(3) = 256^3 = 16777216 --> there are 16777216 possible 3-byte files;
%e A133752 a(4) = 256^4 = 4294967296 --> there are 4294967296 possible 4-byte files;
%e A133752 a(5) = 256^5 = 1099511627776 --> there are 1099511627776 possible 5-byte files.
%t A133752 lst={};Do[AppendTo[lst,256^n],{n,0,4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009 *)
%t A133752 256^Range[0,20] (* _Harvey P. Dale_, Aug 21 2014 *)
%o A133752 (Python)
%o A133752 def A133752(n): return 1<<(n<<3) # _Chai Wah Wu_, Nov 10 2022
%Y A133752 Subsequence of A000079.
%Y A133752 Cf. A218723.
%K A133752 easy,nonn
%O A133752 0,2
%A A133752 Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jan 01 2008
%E A133752 Edited by _Jon E. Schoenfield_, Jan 24 2015