A074535 - OEIS

%I #26 Sep 08 2022 08:45:07

%S 3,14,84,584,4368,33824,266304,2113664,16843008,134480384,1074791424,

%T 8594130944,68736258048,549822930944,4398314962944,35185445863424,

%U 281479271743488,2251816993685504,18014467229220864,144115462954287104

%N a(n) = 2^n + 4^n + 8^n.

%C Number of monic irreducible polynomials of degree 1 in GF(2^n)[x,y,z]. - _Max Alekseyev_, Jan 23 2006

%H Vincenzo Librandi, <a href="/A074535/b074535.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-56,64).

%F G.f.: 1/(1-2*x)+1/(1-4*x)+1/(1-8*x). E.g.f.: exp(2*x)+exp(4*x)+exp(8*x). [_Mohammad K. Azarian_, Dec 26 2008]

%F Let A=[1, 1, 1;2, 0, -2;1, -1, 1], the 3 X 3 Krawtchouk matrix. Then a(n)=trace((A*A')^n). - _Paul Barry_, Sep 18 2004

%t Table[2^n + 4^n + 8^n, {n, 0, 20}]

%o (Magma) [2^n + 4^n + 8^n: n in [0..25]]; // _Vincenzo Librandi_, Jun 11 2011

%o (Python)

%o def a(n): return 2**n + 4**n + 8**n

%o print([a(n) for n in range(20)]) # _Michael S. Branicky_, Mar 14 2021

%Y Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 23 2002