A166122 - OEIS

%I #16 Sep 03 2022 21:04:07

%S 1,2,-3,22,-103,522,-2603,13022,-65103,325522,-1627603,8138022,

%T -40690103,203450522,-1017252603,5086263022,-25431315103,127156575522,

%U -635782877603,3178914388022,-15894571940103,79472859700522

%N a(n) = (7-(-5)^n)/6.

%H G. C. Greubel, <a href="/A166122/b166122.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 (-4,5).

%F a(n) = 5*a(n-2) - 4*a(n-1), a(0)= 1, a(1)= 2, for n>1.

%F a(n) = 7-5*a(n-1), a(0)=1.

%F a(n) = a(n-1)+(-5)^(n-1), a(0)=1.

%F O.g.f.: (1+6*x)/(1+4*x-5*x^2).

%F E.g.f.: (7*exp(x)-exp(-5*x))/6.

%t LinearRecurrence[{-4,5},{1,2},30] (* _Harvey P. Dale_, Mar 10 2016 *)

%t Table[(7 - (-5)^n)/6, {n, 24}] (* or *)

%t CoefficientList[Series[(1 + 6 x)/(1 + 4 x - 5 x^2), {x, 0, 24}], x] (* _Michael De Vlieger_, Apr 27 2016 *)

%Y Cf. A084222, A084247, A166114.

%K sign,easy

%O 0,2

%A _Philippe Deléham_, Oct 07 2009