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%I #45 Feb 06 2024 16:12:54
%S 0,1,7,59,483,3971,32627,268099,2202963,18101731,148741747,1222209539,
%T 10042884243,82522285091,678084838067,5571816717379,45783565402323,
%U 376203124990051,3091257528953587,25400833952575619,208718412957565203,1715037230228712611,14092444741176640307
%N Expansion of x/(1 - 7*x - 10*x^2).
%C Pisano period lengths: 1, 1, 8, 1, 4, 8, 12, 1, 24, 4, 5, 8, 21, 12, 8, 1, 16, 24, 45, 4, ... - _R. J. Mathar_, Aug 10 2012
%C Number of compositions of n-1 into parts 1 (of 7 sorts) and 2 (of 10 sorts). - _Joerg Arndt_, Oct 15 2013
%H Vincenzo Librandi, <a href="/A015568/b015568.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,10).
%F a(n) = 7*a(n-1) + 10*a(n-2).
%F G.f.: Q(0)*x/(2-7*x), where Q(k) = 1 + 1/( 1 - x*(89*k-49)/( x*(89*k+40) - 14/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Oct 14 2013
%t LinearRecurrence[{7, 10}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 14 2012 *)
%t CoefficientList[Series[x/(1-7x-10x^2),{x,0,40}],x] (* _Harvey P. Dale_, Feb 06 2024 *)
%o (Sage) [lucas_number1(n,7,-10) for n in range(0, 20)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 7*Self(n-1) + 10*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-10*x^2))) \\ _G. C. Greubel_, Jan 06 2018
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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