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Expansion of g.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3).
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%I #19 Aug 31 2024 03:10:03

%S 1,6,89,1430,23070,372259,6006853,96927945,1564051382,25237889117,

%T 407244323586,6571387104706,106037398138915,1711043593219257,

%U 27609788897887265,445517838357152822,7188977251094395521,116002973320502471614,1871850382771577632966

%N Expansion of g.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3).

%H G. C. Greubel, <a href="/A100297/b100297.txt">Table of n, a(n) for n = 1..825</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-14,1).

%F a(n) = 17*a(n-1) - 14*a(n-2) + a(n-3).

%F G.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3). - _Colin Barker_, Dec 13 2012

%e a(6) = 372259 = 17*23070 - 14*1430 + 89 = 17*a(5) - 14*a(4) + a(3).

%t LinearRecurrence[{17,-14,1},{1,6,89},20] (* _Harvey P. Dale_, Mar 14 2022 *)

%o (Magma) I:=[1,6,89]; [n le 3 select I[n] else 17*Self(n-1) -14*Self(n-2) +Self(n-3): n in [1..31]]; // _G. C. Greubel_, Feb 05 2023

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A100297

%o if (n<3): return (1,1,6)[n]

%o else: return 17*a(n-1) - 14*a(n-2) + a(n-3)

%o [a(n) for n in range(1,31)] # _G. C. Greubel_, Feb 05 2023

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Nov 11 2004

%E More terms from _Colin Barker_, Dec 13 2012

%E New name using g.f. from _Joerg Arndt_, Aug 31 2024