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%I #20 Feb 27 2024 13:19:26
%S 1,0,4,5,13,17,33,41,66,82,117,142,191,226,290,339,419,483,583,663,
%T 784,884,1027,1148,1317,1460,1656,1825,2049,2245,2501,2725,3014,3270,
%U 3593,3882,4243,4566,4966,5327,5767,6167,6651,7091,7620,8104,8679,9208,9833,10408
%N G.f.: (1-x+2*x^2+2*x^3+2*x^4-x^5+x^6)/((1-x)*(1-x^2)^2*(1-x^3)).
%D H. Gupta, Magic partitions, I, Math. Student 45 (1977), no. 3, 58-62.
%H Vincenzo Librandi, <a href="/A083709/b083709.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,2,1,-1).
%F a(0)=1, a(1)=0, a(2)=4, a(3)=5, a(4)=13, a(5)=17, a(6)=33, a(7)=41, a(n)=a(n-1)+2*a(n-2)-a(n-3)-2*a(n-4)-a(n-5)+2*a(n-6)+a(n-7)-a(n-8). - _Harvey P. Dale_, May 17 2013
%t CoefficientList[Series[(1-x+2x^2+2x^3+2x^4-x^5+x^6)/((1-x) (1-x^2)^2 (1-x^3)), {x,0,60}],x] (* or *) LinearRecurrence[{1,2,-1,-2,-1,2,1,-1},{1,0,4,5,13,17,33,41},60] (* _Harvey P. Dale_, May 17 2013 *)
%o (Magma) I:=[1,0,4,5,13,17,33,41]; [n le 8 select I[n] else Self(n-1)+2*Self(n-2)-Self(n-3)-2*Self(n-4)-Self(n-5)+2*Self(n-6)+Self(n-7)-Self(n-8): n in [1..50]]; // _Vincenzo Librandi_, Sep 09 2016
%o (PARI) Vec((1-x+2*x^2+2*x^3+2*x^4-x^5+x^6)/((1-x)*(1-x^2)^2*(1-x^3)) + O(x^99)) \\ _Altug Alkan_, Sep 09 2016
%Y Cf. A083707.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 15 2003
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