A092811 Expansion of (1-4*x)/(1-8*x).

1, 4, 32, 256, 2048, 16384, 131072, 1048576, 8388608, 67108864, 536870912, 4294967296, 34359738368, 274877906944, 2199023255552, 17592186044416, 140737488355328, 1125899906842624, 9007199254740992, 72057594037927936

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 to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (8).

Formula

a(n) = 8^n/2 + 0^n/2.

a(n) = A001045(3n+1) - A001045(3n-1) + 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

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

Cf. A013731 (same sequence omitting initial 1).

Sequence in context: A213413 A317512 A300177 * A013731 A363440 A009509

Adjacent sequences: A092808 A092809 A092810 * A092812 A092813 A092814

Keyword

easy,nonn

Author

Paul Barry, Mar 10 2004

Status

approved