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G.f.: x*(1+3*x+x^2)/((1-x^2)^2*(1-x^5)).
1

%I #21 Aug 03 2017 13:37:50

%S 0,1,3,3,6,5,10,10,15,15,20,21,28,28,36,35,45,45,55,55,65,66,78,78,91,

%T 90,105,105,120,120,135,136,153,153,171,170,190,190,210,210,230,231,

%U 253,253,276,275,300,300,325,325,350,351,378,378,406,405

%N G.f.: x*(1+3*x+x^2)/((1-x^2)^2*(1-x^5)).

%D S. J. Cyvin et al., Polygonal systems including the corannulene and coronene homologs: novel applications of PĆ³lya's theorem, Z. Naturforsch., 52a (1997), 867-873.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1,1,0,-2,0,1).

%F a(n)=5n/8+39/80+n^2/8+(-1)^n*(n/8+5/16)-(4*A010891(n)+3*A010891(n-1)+2*A010891(n-2)+A010891(n-3))/5. - _R. J. Mathar_, Jun 17 2009

%p A010891 := proc(n) op((n mod 5)+1,[1,-1,0,0,0]) ; end:

%p A038167 := proc(n) 5*n/8+39/80+n^2/8+(-1)^n*(n/8+5/16) -(4*A010891(n)+3*A010891(n-1)+2*A010891(n-2)+A010891(n-3))/5 ; end:

%p seq(A038167(n),n=0..30) ; # _R. J. Mathar_, Jun 17 2009

%t CoefficientList[Series[x (1+3x+x^2)/((1-x^2)^2(1-x^5)),{x,0,60}],x] (* or *) LinearRecurrence[{0,2,0,-1,1,0,-2,0,1},{0,1,3,3,6,5,10,10,15},60] (* _Harvey P. Dale_, Aug 03 2017 *)

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_