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%I #23 Sep 08 2022 08:45:57
%S 0,16,121,512,1562,3888,8403,16384,29524,50000,80525,124416,185646,
%T 268912,379687,524288,709928,944784,1238049,1600000,2042050,2576816,
%U 3218171,3981312,4882812,5940688,7174453,8605184,10255574,12150000,14314575
%N Number of compositions of odd positive integers into 5 parts <= n.
%H Vincenzo Librandi, <a href="/A191902/b191902.txt">Table of n, a(n) for n = 0..10000</a>
%H Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,5,5,-9,5,-1).
%F a(n) = ((n + 1)^5 - (1 + (-1)^n)/2)/2.
%F From _R. J. Mathar_, Jun 22 2011: (Start)
%F a(2n+1) = A191484(2n+1); a(2n) = A191484(2n) - 1.
%F G.f.: x*(16 + 41*x + 51*x^2 + 11*x^3 + x^4) / ( (1+x)*(x-1)^6 ). (End)
%e a(1)=16: the 16 compositions of odd numbers into 5 parts <= 1 are
%e 1: (0,0,0,0,1) --> 5!/(4!1!) = 5;
%e 3: (0,0,1,1,1) --> 5!/(2!3!) = 10;
%e 5: (1,1,1,1,1) --> 5!/(0!5!) = 1.
%t Table[Floor[1/2*((n + 1)^5 - (1 + (-1)^n)/2)], {n, 0, 30}]
%o (Magma) [((n + 1)^5 - (1 + (-1)^n)/2)/2: n in [0..50]]; // _Vincenzo Librandi_, Jul 04 2011
%o (PARI) a(n)=((n+1)^5-(1+(-1)^n)/2)/2 \\ _Charles R Greathouse IV_, Jul 06 2017
%Y Cf. A191484.
%K nonn,easy
%O 0,2
%A _Adi Dani_, Jun 19 2011
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