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%I #22 Dec 28 2022 02:34:11
%S 0,12,173,861,4979,25545,132419,670689,3390203,17039337,85505555,
%T 428366577,2144524907,10730349369,53675623811,268448345025,
%U 1342455212891,6712910908041,33566470310387,167838076383633
%N Expansion of x*(12 +101*x -189*x^2)/((1+2*x)*(1-3*x)*(1-5*x)).
%H G. C. Greubel, <a href="/A120662/b120662.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,1,-30).
%F From _Colin Barker_, Nov 01 2012: (Start)
%F a(n) = 6*a(n-1) + a(n-2) - 30*a(n-3) for n>3.
%F G.f.: x*(12 +101*x -189*x^2)/((1+2*x)*(1-3*x)*(1-5*x)). (End)
%t LinearRecurrence[{6,1,-30},{0,12,173,861},20] (* _Harvey P. Dale_, Jan 09 2019 *)
%o (Magma) I:=[12,173,861]; [0] cat [n le 3 select I[n] else 6*Self(n-1) + Self(n-2) -30*Self(n-3): n in [1..31]]; // _G. C. Greubel_, Dec 25 2022
%o (SageMath)
%o @CachedFunction
%o def a(n): # a = A120662
%o if (n<4): return (0,12,173,861)[n]
%o else: return 6*a(n-1) + a(n-2) -30*a(n-3)
%o [a(n) for n in range(41)] # _G. C. Greubel_, Dec 25 2022
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, Aug 10 2006
%E Edited by _N. J. A. Sloane_, Jul 13 2007
%E Meaningful name using g.f. from _Joerg Arndt_, Dec 26 2022
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