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A239632 Number of parts in all palindromic compositions of n. 2

%I

%S 0,1,3,4,10,12,28,32,72,80,176,192,416,448,960,1024,2176,2304,4864,

%T 5120,10752,11264,23552,24576,51200,53248,110592,114688,237568,245760,

%U 507904,524288,1081344,1114112,2293760,2359296

%N Number of parts in all palindromic compositions of n.

%H Vincenzo Librandi, <a href="/A239632/b239632.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = Sum_{k=1..n}A051159(n,k)*k.

%F a(n) = 4*a(n-2) - 4*a(n-4) for n > 3. - _Giovanni Resta_, Mar 23 2014

%e a(5)=12 because we have: 5, 1+3+1, 2+1+2, 1+1+1+1+1 with a total of 12 parts.

%t nn=30;r=Solve[p==y/(1-x)-y +1+y ^2x^2/(1-x^2)p,p];CoefficientList[Series[D[p/.r,y]/.y->1,{x,0,nn}],x]

%t CoefficientList[Series[(x + 3 x^2 - 2 x^4)/(1 - 2 x^2)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 23 2014 *)

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Mar 22 2014

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)