A074535 a(n) = 2^n + 4^n + 8^n.

3, 14, 84, 584, 4368, 33824, 266304, 2113664, 16843008, 134480384, 1074791424, 8594130944, 68736258048, 549822930944, 4398314962944, 35185445863424, 281479271743488, 2251816993685504, 18014467229220864, 144115462954287104

Offset: 0

Author

Robert G. Wilson v, Aug 23 2002

Keywords

• easy
• nonn

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

Crossrefs

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

Programs

Magma

[2^n + 4^n + 8^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica

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

Python

def a(n): return 2**n + 4**n + 8**n
print([a(n) for n in range(20)]) # Michael S. Branicky, Mar 14 2021

Formula

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]

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