login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053601 Number of bases of an n-dimensional vector space over GF(2). 11
1, 1, 3, 28, 840, 83328, 27998208, 32509919232, 132640470466560, 1927943976061501440, 100981078400558897823744, 19242660536873338307044442112, 13448310596010038676027219703234560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge 1986

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..59

Claude Carlet, Philippe Gaborit, Jon-Lark Kim and Patrick Sole, A new class of codes for Boolean masking of cryptographic computations, arXiv:1110.1193 [cs.IT], 2011-2012.

David Ellerman, The number of direct-sum decompositions of a finite vector space, arXiv:1603.07619 [math.CO], 2016.

David Ellerman, The Quantum Logic of Direct-Sum Decompositions, arXiv:1604.01087 [quant-ph], 2016.

FORMULA

a(n) = (2^n-1)(2^n-2)...(2^n-2^(n-1))/n! = A002884(n)/n!.

EXAMPLE

a(2)=3 because the 3 bases are {01,10}, {01,11}, {10,11}.

MATHEMATICA

Table[Product[2^n - 2^k, {k, 0, n-1}]/n!, {n, 0, 20}] (* G. C. Greubel, May 16 2019 *)

PROG

(PARI) a(n) = prod(k=0, n-1, 2^n - 2^k)/n!; \\ Michel Marcus, Mar 25 2016

(MAGMA) [1] cat [(&*[2^n -2^k: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, May 16 2019

(Sage) [product(2^n -2^k for k in (0..n-1))/factorial(n) for n in (0..20)] # G. C. Greubel, May 16 2019

CROSSREFS

Cf. A002884.

Sequence in context: A276745 A015474 A324462 * A140990 A196735 A208438

Adjacent sequences:  A053598 A053599 A053600 * A053602 A053603 A053604

KEYWORD

easy,nonn

AUTHOR

Fred Galvin (galvin(AT)math.ukans.edu), Jan 20 2000

EXTENSIONS

More terms from Vladeta Jovovic, Apr 05 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)