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A097896 Number of compositions of n with either all parts odd or all parts even. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 07:17 EDT 2021. Contains 343909 sequences. (Running on oeis4.)