login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302339 Triangle read by rows: T(n,k) = number of linear operators T on an n-dimensional vector space over GF(2) such that U is invariant under T for some given k-dimensional subspace U. 1
1, 2, 2, 16, 8, 16, 512, 128, 128, 512, 65536, 8192, 4096, 8192, 65536, 33554432, 2097152, 524288, 524288, 2097152, 33554432, 68719476736, 2147483648, 268435456, 134217728, 268435456, 2147483648, 68719476736 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A subspace U is invariant under operator T if T(u) is in U for all u in U.

Main diagonal is A002416(n).

LINKS

Table of n, a(n) for n=0..27.

FORMULA

T(n,k) = 2^(k^2)*2^(n(n-k)).

EXAMPLE

         1;

         2,       2;

        16,       8,     16;

       512,     128,    128,    512;

     65536,    8192,   4096,   8192,   65536;

  33554432, 2097152, 524288, 524288, 2097152, 33554432;

MATHEMATICA

Clear[t]; t[n_, k_] := q^(k^2) q^(n (n - k));

Table[Table[t[n, k], {k, 0, n}], {n, 0, 5}] /. q -> 2 // Grid

PROG

(MAGMA) /* As triangle */ [[2^(k^2)*2^(n*(n-k)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Apr 08 2018

CROSSREFS

Cf. A302346.

Sequence in context: A097540 A112327 A152541 * A093114 A016740 A193145

Adjacent sequences:  A302336 A302337 A302338 * A302340 A302341 A302342

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Apr 05 2018

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 May 16 00:49 EDT 2021. Contains 343937 sequences. (Running on oeis4.)