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%I #36 Dec 30 2023 23:41:28
%S 0,1,7,52,385,2851,21112,156337,1157695,8572876,63483217,470101147,
%T 3481157680,25778407201,190892323447,1413581485732,10467747370465,
%U 77514976050451,574008074464552,4250601449403217,31476234369216175
%N Expansion of x/(1 - 7*x - 3*x^2).
%H Vincenzo Librandi, <a href="/A015559/b015559.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 (7,3).
%F a(n) = 7*a(n-1) + 3*a(n-2).
%t Join[{a=0,b=1},Table[c=7*b+3*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 17 2011 *)
%t LinearRecurrence[{7, 3}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 14 2012 *)
%t CoefficientList[Series[x/(1-7x-3x^2),{x,0,30}],x] (* _Harvey P. Dale_, Nov 12 2017 *)
%o (Sage) [lucas_number1(n,7,-3) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 7*Self(n-1) + 3*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-3*x^2))) \\ _G. C. Greubel_, Dec 30 2017
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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