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%I #13 Jun 13 2015 00:49:10
%S 1,1,1,2,2,2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,24,27,30,33,37,40,43,
%T 47,51,55,60,65,70,75,80,86,92,98,105,112,119,126,134,142,150,159,168,
%U 177,187,197,207,218,229,240,252
%N Expansion of 1/((1-x)(1-x^3)(1-x^7)(1-x^8)).
%C Number of partitions of n into parts 1, 3, 7, and 8. - _Joerg Arndt_, Jun 28 2013
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,0,1,0,-1,-1,0,1,0,0,-1,1,0,1,-1).
%F a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=4, a(8)=5, a(9)=6, a(10)=7, a(11)=8, a(12)=9, a(13)=10, a(14)=12, a(15)=14, a(16)=16, a(17)=18, a(18)=20, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-7)- a(n-9)- a(n-10)+a(n-12)-a(n-15)+a(n-16)+a(n-18)-a(n-19) [_Harvey P. Dale_, Mar 10 2012]
%F a(n) = floor((504*((floor((n+2)/2)-2*floor((n+2)/4))*(-1)^floor(n/4))+2*n^3+57*n^2+480*n+2088)/2016). - _Tani Akinari_, Jun 28 2013
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^7)(1-x^8)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,1,-1,0,0,1,0,-1,-1,0,1,0,0,-1,1,0,1,-1},{1,1,1,2,2,2,3,4,5,6,7,8,9,10,12,14,16,18,20},61] (* _Harvey P. Dale_, Mar 10 2012 *)
%o (PARI) a(n)=(2*n^3+57*n^2+480*n+2088+(n%4<2)*(-1)^(n\4)*504)\2016 \\ _Charles R Greathouse IV_, Jun 28 2013
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_.
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