A175772 - OEIS

%I #21 Sep 08 2022 08:45:51

%S 1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,11,13,16,20,25,31,38,46,55,67,81,

%T 98,119,145,177,216,263,320,389,473,575,699,850,1034,1258,1530,1862,

%U 2265,2755,3351,4076,4958,6031,7336,8923,10854,13203,16060,19535,23762

%N Expansion of 1/(1 - x - x^9 - x^17 + x^18).

%C The ratio a(n+1)/a(n) is 1.216391661138265... as n->infinity.

%H G. C. Greubel, <a href="/A175772/b175772.txt">Table of n, a(n) for n = 0..1000</a>

%H Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,-1).

%F G.f.: 1/((1 - x^2 + x^4)*(1 - x^4 - x^5 - x^6 + x^10)*(1 - x + x^2 - x^3 + x^4)).

%F a(n) = a(n-1) + a(n-9) + a(n-17) - a(n-18). - _Harvey P. Dale_, Jul 13 2014

%t CoefficientList[Series[1/(1 - x - x^9 - x^17 + x^18), {x, 0, 50}], x] (* or *)

%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11} ,60] (* _Harvey P. Dale_, Jul 13 2014 *)

%o (PARI) x='x+O('x^50); Vec(1/(1-x-x^9-x^17+x^18)) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^9-x^17+x^18))); // _G. C. Greubel_, Nov 03 2018

%Y Cf. A175739.

%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

%K nonn,easy

%O 0,10

%A _Roger L. Bagula_, Dec 04 2010