OFFSET
0,2
COMMENTS
4th binomial transform of (1,0,16,0,256,...).
Number of compositions of even natural numbers into n parts <= 7. - Adi Dani, May 28 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (8).
FORMULA
a(n) = 8^n/2 + 0^n/2.
a(n) = A013731(n-1), n > 0. - R. J. Mathar, Sep 08 2008
a(n) = 4 * 8^(n-1), a(0)=1. - Vincenzo Librandi, Jun 16 2011
a(n) = Sum_{k=0..n} A134309(n,k)*4^k = Sum_{k=0..n} A055372(n,k)*3^k. - Philippe Deléham, Feb 04 2012
E.g.f.: (1 + exp(8*x))/2. - Stefano Spezia, May 29 2024
EXAMPLE
From Adi Dani, May 28 2011: (Start)
a(2)=32: there are 32 compositions of even natural numbers into 2 parts <= 7:
(0,0);
(0,2),(2,0),(1,1);
(0,4),(4,0),(1,3),(3,1),(2,2);
(0,6),(6,0),(1,5),(5,1),(2,4),(4,2),(3,3);
(1,7),(7,1),(2,6),(6,2),(3,5),(5,3),(4,4);
(3,7),(7,3),(4,6),(6,4),(5,5);
(5,7),(7,5),(6,6);
(7,7). (End)
MATHEMATICA
Table[EulerPhi[8^n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)
PROG
(Magma) [8^n/2+0^n/2: n in [0..20]]; // Vincenzo Librandi, Jun 16 2011
(PARI) a(n)=max(1, 8^n/2) \\ Charles R Greathouse IV, Apr 09 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 10 2004
STATUS
approved