A092533 G.f.: (1+x^8)/((1-x)*(1-x^4)).

1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 10, 12, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 18, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 26, 26, 26, 26, 28, 28, 28, 28, 30, 30, 30, 30, 32, 32, 32, 32, 34, 34, 34, 34, 36, 36, 36, 36, 38, 38

Offset: 0

Author

N. J. A. Sloane, Apr 08 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Programs

Magma

I:=[1,1,1,1,2,2,2,2,4]; [n le 9 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..30]]; // Vincenzo Librandi, Jul 25 2014

Mathematica

CoefficientList[Series[(1+x^8)/((1-x)(1-x^4)),{x,0,100}],x] (* or *) Join[{1,1,1,1},LinearRecurrence[{1,0,0,1,-1},{2,2,2,2,4},80]] (* Harvey P. Dale, Jul 25 2014 *)

Formula

a(n) = 1 for n<4, a(n) = 2*floor(n/4) for n>=4. - Ralf Stephan, Apr 29 2014