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%I #17 Sep 08 2022 08:45:47
%S 1,6,24,156,564,4116,12804,110676,273444,3046836,5156484,86248596,
%T 68445924,2519011956,-465634236,76035992916,-90005019996,
%U 2371084807476,-5071235407356,76203779631636,-228340841852316,2514454230801396
%N a(0)=1, a(1)=6, a(n) = 30*a(n-2) - a(n-1).
%C a(n)/a(n-1) tends to -6.
%H G. C. Greubel, <a href="/A165491/b165491.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 (-1, 30).
%F G.f.: (1+7*x)/(1+x-30*x^2).
%F a(n) = Sum_{k=0..n} A112555(n,k)*5^k.
%F a(n) = (12*5^n-(-6)^n)/11. - _Klaus Brockhaus_, Sep 26 2009
%F E.g.f.: (12*exp(5*x) - exp(-6*x))/11. - _G. C. Greubel_, Oct 20 2018
%p seq(coeff(series((1+7*x)/(1+x-30*x^2),x,n+1), x, n), n = 0 .. 22); # _Muniru A Asiru_, Oct 21 2018
%t LinearRecurrence[{-1,30},{1,6},30] (* _Harvey P. Dale_, May 04 2012 *)
%o (PARI) vector(30, n, n--; (12*5^n-(-6)^n)/11) \\ _G. C. Greubel_, Oct 20 2018
%o (Magma) [(12*5^n-(-6)^n)/11: n in [0..30]]; // _G. C. Greubel_, Oct 20 2018
%o (GAP) a:=[1,6];; for n in [3..22] do a[n]:=30*a[n-2]-a[n-1]; od; a; # _Muniru A Asiru_, Oct 21 2018
%K easy,sign
%O 0,2
%A _Philippe Deléham_, Sep 21 2009