A097896 Number of compositions of n with either all parts odd or all parts even.

1, 2, 2, 5, 5, 12, 13, 29, 34, 71, 89, 176, 233, 441, 610, 1115, 1597, 2840, 4181, 7277, 10946, 18735, 28657, 48416, 75025, 125489, 196418, 326003, 514229, 848424, 1346269, 2211077, 3524578, 5768423, 9227465, 15061424, 24157817, 39350313

Offset

1,2

Comments

Number of compositions of n with only even parts is 0 if n is odd, or 2^((n-2)/2) if n is even.

Links

Table of n, a(n) for n=1..38.

Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2).

Formula

a(2*n-1) = Fibonacci(2*n-1), a(2*n) = 2^(n-1)+Fibonacci(2*n). - Vladeta Jovovic, Sep 05 2004

a(n)= +a(n-1) +3*a(n-2) -2*a(n-3) -2*a(n-4). G.f.: -x*(-1-x+x^3+3*x^2)/ ((2*x^2-1) * (x^2+x-1)). - R. J. Mathar, Feb 06 2010

Example

For n=4: 1+1+1+1, 3+1, 1+3, 2+2, 4: total=5 so a(n)=5.

Mathematica

f[n_] := Block[{}, Fibonacci[n] + If[EvenQ[n], 2^(n/2 - 1), 0]]; Table[ f[n], {n, 22}] (* Robert G. Wilson v, Sep 06 2004 *)
LinearRecurrence[{1, 3, -2, -2}, {1, 2, 2, 5}, 40] (* Harvey P. Dale, Nov 27 2012 *)

Crossrefs

Cf. A096441, A000045.

Sequence in context: A032580 A002014 A135153 * A030223 A300436 A056504

Adjacent sequences: A097893 A097894 A097895 * A097897 A097898 A097899

Keyword

nonn

Author

Dubois Marcel (dubois.ml(AT)club-internet.fr), Sep 03 2004

Extensions

More terms from Robert G. Wilson v, Sep 06 2004

Status

approved