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a(0) = 5, a(1) = 5, and a(n) = 4*a(n-1) - a(n-2) - 4 for n >= 2.
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%I #8 Jan 22 2022 19:41:50

%S 5,5,11,35,125,461,1715,6395,23861,89045,332315,1240211,4628525,

%T 17273885,64467011,240594155,897909605,3351044261,12506267435,

%U 46674025475,174189834461,650085312365,2426151414995,9054520347611,33791929975445,126113199554165,470660868241211,1756530273410675,6555460225401485,24465310628195261,91305782287379555

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

%C One of 10 linear second-order recurrence sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4 and together forming A350916.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).

%F a(n) = 3*A001835(n) + 2. - _Hugo Pfoertner_, Jan 22 2022

%F G.f.: (5 - 20*x + 11*x^2)/((1 - x)*(1 - 4*x + x^2)). - _Stefano Spezia_, Jan 22 2022

%Y Cf. A001835, A350916.

%Y Other sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4: A103974, A350917, A350919, A350921, A350922, A350923, A350924, A350925, A350926.

%K nonn,easy

%O 0,1

%A _Max Alekseyev_, Jan 22 2022