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a(n) = (4^n+8*(-5)^n)/9.
6

%I #19 Feb 18 2018 02:44:33

%S 1,-4,24,-104,584,-2664,14344,-67624,354504,-1706984,8797064,

%T -42936744,218878024,-1077612904,5455173384,-27007431464,136110899144,

%U -676259528424,3398477511304,-16923668079784

%N a(n) = (4^n+8*(-5)^n)/9.

%H Harvey P. Dale, <a href="/A166036/b166036.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 (-1,20).

%F a(n) = -a(n-1) + 20*a(n-2), a(0) = 1, a(1) = -4, for n>1.

%F a(n) = Sum_{k=0..n} A112555(n,k)*(-5)^k.

%F G.f.: (1-3x)/(1+x-20x^2).

%F E.g.f.: (1/9)*(exp(4*x) + 8*exp(-5*x)). - _G. C. Greubel_, Apr 24 2016

%t Table[(4^n+8(-5)^n)/9,{n,0,30}] (* or *) LinearRecurrence[{-1,20},{1,-4},30] (* _Harvey P. Dale_, Mar 05 2016 *)

%o (PARI) vector(100, n, n--; (4^n+8*(-5)^n)/9) \\ _Altug Alkan_, Apr 24 2016

%Y Cf. A077925, A091004, A166035.

%K easy,sign

%O 0,2

%A _Philippe Deléham_, Oct 05 2009