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%I #21 Aug 24 2017 14:47:38
%S 1,12,103,774,5425,36456,238267,1527258,9651829,60352380,374321311,
%T 2306963022,14146953913,86407602384,526075008835,3194597025666,
%U 19358317017277,117103576420068,707389830102439,4268180838524790,25728294320699521,154965812371951032
%N Expansion of 1/((1-x)*(1-5*x)(1-6*x)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-41,30).
%F a(n) = (1/20)-(25/4)*5^n+(36/5)*6^n. [_Antonio Alberto Olivares_, Feb 06 2010]
%F a(0)=1, a(1)=12, a(n)=11*a(n-1)-30*a(n-2)+1. - _Vincenzo Librandi_, Feb 10 2011
%p a:=n->sum(6^(n-j)-5^(n-j),j=0..n): seq(a(n), n=1..19); # _Zerinvary Lajos_, Jan 15 2007
%t Table[(2^(n + 3)*3^(n + 1) - 5^(n + 2) + 1)/20, {n, 40}] (* and *) CoefficientList[Series[1/((1 - z) (1 - 5*z) (1 - 6*z)), {z, 0, 40}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)
%t LinearRecurrence[{12,-41,30},{1,12,103},30] (* _Harvey P. Dale_, Aug 24 2017 *)
%o (PARI) Vec(1/((1-x)*(1-5*x)(1-6*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A016218.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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