login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038521 Number of elements of GF(2^n) with trace 1 and subtrace 1. 5
0, 2, 1, 4, 10, 12, 36, 64, 120, 272, 496, 1024, 2080, 4032, 8256, 16384, 32640, 65792, 130816, 262144, 524800, 1047552, 2098176, 4194304, 8386560, 16781312, 33550336, 67108864, 134225920, 268419072, 536887296, 1073741824, 2147450880 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
K. Cattel, C. R. Miers, F. Ruskey, J. Sawada, M. Serra, The number of irreducible polynomials over Gf(2) with given trace and subtrace, J. Combin. Math. Combin. Comput. 47 (2003) 31-64. [From R. J. Mathar, Oct 20 2008]
FORMULA
a(n) = C(n, r+0) + C(n, r+4) + C(n, r+8) + ... where r = 3 if n odd, r = 1 if n even.
From Colin Barker, Aug 02 2019: (Start)
G.f.: x*(2 + x) / ((1 - 2*x)*(1 + 2*x + 2*x^2)).
a(n) = ((-1-i)^(-1+n) + (-1+i)^(-1+n) + 2^n) / 2.
a(n) = 2*a(n-2) + 4*a(n-3) for n>2.
(End)
MAPLE
A038521 := proc(n) local r, a, i ; if n mod 2 = 1 then r := 3 ; else r := 1 ; fi; a :=0 ; for i from r to n by 4 do a := a+binomial(n, i) ; od; a ; end: for n from 1 to 40 do printf("%d, ", A038521(n)) ; od: # R. J. Mathar, Oct 20 2008
MATHEMATICA
LinearRecurrence[{0, 2, 4}, {0, 2, 1}, 33] (* Jean-François Alcover, May 08 2023 *)
PROG
(PARI) concat(0, Vec(x*(2 + x) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^35))) \\ Colin Barker, Aug 02 2019
(Magma) I:=[0, 2, 1]; [m le 3 select I[m] else 2*Self(m-2) + 4*Self(m-3): m in [1..33]] // Marius A. Burtea, Aug 02 2019
CROSSREFS
Cf. A134654. - R. J. Mathar, Oct 20 2008
Sequence in context: A212770 A205855 A329709 * A134654 A198262 A085421
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Values duplicated A038520 and were replaced by R. J. Mathar, Oct 20 2008
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 14:49 EST 2023. Contains 367680 sequences. (Running on oeis4.)