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A107480 a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).

%I A107480 #38 Sep 08 2022 08:45:18
%S A107480 0,1,1,2,3,5,8,14,25,42,71,121,207,353,601,1025,1748,2980,5080,8661,
%T A107480 14767,25176,42922,73178,124762,212707,362644,618273,1054096,1797131,
%U A107480 3063933,5223708,8905915,15183719,25886764,44134416,75244889,128285220,218713827
%N A107480 a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).
%C A107480 Lim_{n->infinity} a(n)/a(n-1) = 1.70490277..., the real root of x^5 = x^4 + x^3 + 1.
%H A107480 Harvey P. Dale, <a href="/A107480/b107480.txt">Table of n, a(n) for n = 0..1000</a>
%H A107480 Peter Borwein and Kevin G. Hare, <a href="http://docserver.carma.newcastle.edu.au/225/2/00_148-Borwein-Hare.pdf">Some computations on Pisot and Salem numbers</a>, 2000, table 1, p. 7.
%H A107480 Peter Borwein and Kevin G. Hare, <a href="https://doi.org/10.1090/S0025-5718-01-01336-9">Some computations on the spectra of Pisot and Salem numbers</a>, Math. Comp. 71 (2002), 767-780.
%H A107480 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1,1,0,1).
%F A107480 G.f.: x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)). - _Colin Barker_, Dec 17 2017
%t A107480 LinearRecurrence[{1,0,1,1,1,0,1}, {0,1,1,2,3,5,8}, 50] (* _Harvey P. Dale_, May 21 2012 *)
%o A107480 (PARI) concat([0], Vec(x*(1 + x^2 - x^5) / ((1 + x^2)*(1 - x - x^2 - x^5)) + O(x^40))) \\ _Colin Barker_, Dec 17 2017
%o A107480 (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1 +x^2-x^5)/((1+x^2)*(1-x-x^2-x^5)))); // _G. C. Greubel_, Nov 03 2018
%Y A107480 Cf. A013984.
%Y A107480 Cf. A107479, A109538, A109543, A109544, A114749, A125950, A130844, A143335, A147851.
%K A107480 nonn,easy,less
%O A107480 0,4
%A A107480 _Roger L. Bagula_, May 27 2005
%E A107480 Entry rewritten by _Charles R Greathouse IV_, Jan 26 2011