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%I #23 Jul 30 2015 22:18:45
%S 1,0,0,1,0,1,1,0,2,1,1,2,1,2,2,2,3,2,3,3,3,4,3,4,5,4,5,5,5,6,6,6,7,7,
%T 7,8,8,8,9,9,10,10,10,11,11,12,12,12,14,13,14,15,14,16,16,16,18,17,18,
%U 19,19,20,20,21,22,22,23,23
%N Expansion of 1/((1-x^3)(1-x^5)(1-x^8)).
%C Partitions of n into parts 3, 5 and 8. - _David Neil McGrath_, Sep 03 2014
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1).
%F a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=1, a(7)=0, a(8)=2, a(9)=1, a(10)=1, a(11)=2, a(12)=1, a(13)=2, a(14)=2, a(15)=2, a(n)=a(n-3)+ a(n-5)-a(n-11)-a(n-13)+a(n-16). - _Harvey P. Dale_, Jan 18 2014
%F a(n) = floor((1/240)*n^2+(1/15)*n+3/4+(1/27)*cos((1/4)*n*Pi)+(1/5)*cos((3/4)*n*Pi)+(1/5)*cos((5/4)*n*Pi)+(1/27)*cos((7/4)*n*Pi)-(1/31)*sin((2/5)*n*Pi)+(1/7)*sin((4/5)*n*Pi)-(1/7)*sin((6/5)*n*Pi)+(1/31)*sin((8/5)*n*Pi)+(1/22)*cos((2/5)*n*Pi)-(1/22)*cos((4/5)*n*Pi)-(1/22)*cos((6/5)*n*Pi)+(1/22)*cos((8/5)*n*Pi)). - _Robert Israel_, Sep 03 2014
%p f:= LREtools[REtoproc](a(n)=a(n-3)+ a(n-5)-a(n-11)-a(n-13)+a(n-16),a(n),{a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=1, a(7)=0, a(8)=2, a(9)=1, a(10)=1, a(11)=2, a(12)=1, a(13)=2, a(14)=2, a(15)=2}):
%p seq(f(n),n=0..100); # _Robert Israel_, Sep 03 2014
%t CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^8)),{x,0,70}],x] (* or *) LinearRecurrence[{0,0,1,0,1,0,0,0,0,0,-1,0,-1,0,0,1},{1,0,0,1,0,1,1,0,2,1,1,2,1,2,2,2},70] (* _Harvey P. Dale_, Jan 18 2014 *)
%K nonn
%O 0,9
%A _N. J. A. Sloane_.
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