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A191899 Number of compositions of odd natural numbers into 8 parts <=n 0

%I

%S 0,128,3280,32768,195312,839808,2882400,8388608,21523360,50000000,

%T 107179440,214990848,407865360,737894528,1281445312,2147483648,

%U 3487878720,5509980288,8491781520,12800000000,18911429680,27437936768,39155492640,55037657088,76293945312,104413532288

%N Number of compositions of odd natural numbers into 8 parts <=n

%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_10">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,48,-42,0,42,-48,27,-8,1).

%F a(n) = 1/2*((n + 1)^8 - (1 + (-1)^n)/2).

%F G.f.: -16*x*(8*x^6+141*x^5+624*x^4+974*x^3+624*x^2+141*x+8) / ((x-1)^9*(x+1)). - _Colin Barker_, May 16 2013

%e a(1)=128 compositions of odd numbers into 8 parts <=1

%e 1:(0,0,0,0,0,0,0,1)-->8!/(7!1!)= 8

%e 3:(0,0,0,0,0,1,1,1)-->8!/(5!3!)=56

%e 5:(0,0,0,1,1,1,1,1)-->8!/(3!5!)=56

%e 7:(0,1,1,1,1,1,1,1)-->8!/(1!7!)= 8

%e -------------------------------------

%e 128

%t Table[Floor[1/2*((n + 1)^8 - (1 + (-1)^n)/2)], {n, 0, 25}]

%t LinearRecurrence[{8,-27,48,-42,0,42,-48,27,-8,1},{0,128,3280,32768,195312,839808,2882400,8388608,21523360,50000000},30] (* _Harvey P. Dale_, Aug 30 2016 *)

%o (PARI) a(n)=1/2*((n+1)^8-(1+(-1)^n)/2) \\ _Charles R Greathouse IV_, Jul 06 2017

%K nonn,easy

%O 0,2

%A _Adi Dani_, Jun 19 2011

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Last modified June 19 13:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)