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Expansion of 1/(1 - x^4 - x^5 - x^6 + x^10).
1

%I #30 Dec 02 2017 03:29:19

%S 1,0,0,0,1,1,1,0,1,2,2,2,2,3,4,5,5,7,8,10,12,15,18,22,26,32,40,48,58,

%T 70,86,105,128,154,188,229,279,339,412,501,610,742,902,1098,1335,1624,

%U 1975,2403,2923,3556,4324

%N Expansion of 1/(1 - x^4 - x^5 - x^6 + x^10).

%C Lim_{n->infinity} a(n)/a(n+1) = 0.8221036... (the smallest real root of 1 - x^4 - x^5 - x^6 + x^10). - _Iain Fox_, Nov 30 2017

%H Iain Fox, <a href="/A147652/b147652.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1,1,0,0,0,-1).

%F G.f.: 1/(1 - x^4 - x^5 - x^6 + x^10).

%F a(n) = a(n-4) + a(n-5) + a(n-6) - a(n-10), n > 9. - _Iain Fox_, Nov 30 2017

%t CoefficientList[Series[1/(1-x^4-x^5-x^6+x^10),{x,0,50}],x] (* or *) LinearRecurrence[{0,0,0,1,1,1,0,0,0,-1},{1,0,0,0,1,1,1,0,1,2},60] (* _Harvey P. Dale_, Jun 24 2017 *)

%o (PARI) first(n) = Vec(1/(1 - x^4 - x^5 - x^6 + x^10) + O(x^n)) \\ _Iain Fox_, Nov 30 2017

%K nonn,easy

%O 0,10

%A _Roger L. Bagula_, Nov 09 2008

%E Definition corrected by _N. J. A. Sloane_, Nov 10 2008