|
%I #14 Oct 24 2017 17:59:42
%S 1,1,1,1,1,2,2,2,3,3,4,4,4,5,5,6,7,7,8,8,9,10,10,11,12,13,14,14,15,16,
%T 17,18,19,20,21,22,23,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42,43,
%U 45,46,48,50,51,53,54,56
%N Expansion of 1/((1-x)(1-x^5)(1-x^8)).
%C Number of partitions of n into parts 1, 5 and 8. - _Michel Marcus_, Oct 12 2014
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 0, -1, 1).
%F a(n)= +a(n-1) +a(n-5) -a(n-6) +a(n-8) -a(n-9) -a(n-13) +a(n-14). - _R. J. Mathar_, Aug 21 2014
%F a(n) = floor(n*(n+14)/80+1). - _Tani Akinari_, Oct 12 2014
%t CoefficientList[Series[1/((1-x)(1-x^5)(1-x^8)),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,0,0,1,-1,0,1,-1,0,0,0,-1,1},{1,1,1,1,1,2,2,2,3,3,4,4,4,5},80] (* _Harvey P. Dale_, Oct 24 2017 *)
%o (PARI) Vec(1/((1-x)*(1-x^5)*(1-x^8)) + O(x^100)) \\ _Michel Marcus_, Oct 12 2014
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_.
|
