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%I #16 Sep 04 2017 02:22:28
%S 1,1,1,2,3,3,4,6,7,8,10,12,14,16,19,22,25,28,32,36,40,45,50,55,61,67,
%T 73,80,88,95,103,112,121,130,140,151,162,173,185,198,211,224,239,254,
%U 269,285,302,319,337,356,375,395
%N Expansion of 1/((1-x)(1-x^3)(1-x^4)(1-x^7)).
%C Number of partitions of n into parts 1, 3, 4 and 7. - _Ilya Gutkovskiy_, May 14 2017
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 1, -1).
%F a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=3, a(6)=4, a(7)=6, a(8)=7, a(9)=8, a(10)=10, a(11)=12, a(12)=14, a(13)=16, a(14)=19, a(n) = a(n-1) + a(n-3) - a(n-5) - a(n-10) + a(n-12) + a(n-14) - a(n-15). - _Harvey P. Dale_, Feb 26 2012
%p M := Matrix(15, (i,j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 12, 14])) then 1 elif j=1 and member(i, [5, 10, 15]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..51); # _Alois P. Heinz_, Jul 25 2008
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^7)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,1,0,-1,0,0,0,0,-1,0,1,0,1,-1},{1,1,1,2,3,3,4,6,7,8,10,12,14,16,19},60] (* _Harvey P. Dale_, Feb 26 2012 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_