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%I #23 Apr 19 2023 07:56:56
%S 1,5,13,27,45,67,95,125,163,201,249,295,353,407,475,537,615,685,773,
%T 851,949,1035,1143,1237,1355,1457,1585,1695,1833,1951,2099,2225,2383,
%U 2517,2685,2827,3005,3155,3343,3501,3699,3865,4073,4247,4465,4647,4875,5065
%N Crystal ball sequence for planar net 3.6.3.6.
%H T. D. Noe, <a href="/A008580/b008580.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F G.f.: [(1+2x)(1+2x+2x^2+2x^3-x^4)]/[(1-x)^3(1+x)^2]. - _Ralf Stephan_, Apr 24 2004
%F From _Colin Barker_, Jan 26 2016: (Start)
%F a(n) = (18*n^2+2*(-1)^n*n+18*n-7*(-1)^n-1)/8 for n>0.
%F a(n) = (9*n^2+10*n-4)/4 for n>0 and even.
%F a(n) = (9*n^2+8*n+3)/4 for n odd. (End)
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Apr 19 2023
%t Join[{1},LinearRecurrence[{1,2,-2,-1,1},{5,13,27,45,67},40]] (* _Harvey P. Dale_, Dec 03 2014 *)
%o (PARI) a(n)=abs([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; 1,-1,-2,2,1]^n*[-1;5;13;27;45])[1,1] \\ _Charles R Greathouse IV_, Jun 16 2015
%o (PARI) Vec((1+2*x)*(1+2*x+2*x^2+2*x^3-x^4)/((1-x)^3*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 26 2016
%K nonn,nice,easy
%O 0,2
%A _N. J. A. Sloane_
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