A166152 - OEIS

%I #11 Jun 30 2023 14:28:58

%S 1,-6,48,-300,2316,-14916,112188,-738660,5450556,-36474276,265397628,

%T -1797317220,12944017596,-88431340836,632080079868,-4346196394980,

%U 30893559749436,-213433808338596,1510963317814908

%N a(n) = (6^n+12*(-7)^n)/13.

%H G. C. Greubel, <a href="/A166152/b166152.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, 42).

%F a(n) = 42*a(n-2)-a(n-1), a(0)= 1, a(1)= -6, for n>1.

%F G.f.: (1-5x)/(1+x-42*x^2).

%F a(n)= Sum_{k, 0<=k<=n} A112555(n,k)*(-7)^k.

%F E.g.f.: (1/13)*(exp(6*x) + 12*exp(-7*x)). - _G. C. Greubel_, May 01 2016

%t LinearRecurrence[{-1,42}, {1,-6}, 50] (* _G. C. Greubel_, May 01 2016 *)

%t Table[(6^n+12*(-7)^n)/13,{n,0,30}] (* _Harvey P. Dale_, Jun 01 2019 *)

%o (PARI) a(n)=(6^n+12*(-7)^n)/13 \\ _Charles R Greathouse IV_, May 02 2016

%Y Cf. A166035, A166036, A166149.

%K easy,sign

%O 0,2

%A _Philippe Deléham_, Oct 08 2009