A368484 - OEIS

%I #7 Dec 27 2023 10:26:30

%S 1,0,1,1,5,8,24,44,108,208,464,912,1936,3840,7936,15808,32192,64256,

%T 129792,259328,521472,1042432,2091008,4180992,8375296,16748544,

%U 33525760,67047424,134156288,268304384,536739840,1073463296,2147205120,4294377472,8589344768

%N Number of compositions (ordered partitions) of n into parts not greater than n/2.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-8,-4,8).

%F G.f.: (1 - 2*x - 3*x^2 + 7*x^3 + 3*x^4 - 6*x^5) / ((1 - 2*x) * (1 - 2*x^2)^2).

%F a(n) = [x^n] 1 / (1 - Sum_{1 <= j <= n/2} x^j).

%t CoefficientList[Series[(1 - 2 x - 3 x^2 + 7 x^3 + 3 x^4 - 6 x^5)/((1 - 2 x) (1 - 2 x^2)^2), {x, 0, 34}], x]

%t Join[{1}, LinearRecurrence[{2, 4, -8, -4, 8}, {0, 1, 1, 5, 8}, 34]]

%Y Cf. A011782, A110618, A258259.

%K nonn,easy

%O 0,5

%A _Ilya Gutkovskiy_, Dec 26 2023