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a(0) = 3, a(1) = 3, and a(n) = 6*a(n-1) - a(n-2) - 4 for n >= 2.
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%I #11 Jan 22 2022 19:41:58

%S 3,3,11,59,339,1971,11483,66923,390051,2273379,13250219,77227931,

%T 450117363,2623476243,15290740091,89120964299,519435045699,

%U 3027489309891,17645500813643,102845515571963,599427592618131,3493720040136819,20362892648202779,118683635849079851,691738922446276323

%N a(0) = 3, a(1) = 3, and a(n) = 6*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 (7,-7,1).

%F G.f.: (3 - 18*x + 11*x^2)/((1 - x)*(1 - 6*x + x^2)). - _Stefano Spezia_, Jan 22 2022

%F a(n) = 2*A001653(n) + 1 = 4*A011900(n-1) - 1 for n >= 1. - _Hugo Pfoertner_, Jan 22 2022

%Y Cf. A001653, A011900, A350916.

%Y Other sequences satisfying (a(n)*a(n-1)-1) * (a(n)*a(n+1)-1) = (a(n)+1)^4: A103974, A350917, A350919, A350920, A350922, A350923, A350924, A350925, A350926.

%K nonn,easy

%O 0,1

%A _Max Alekseyev_, Jan 22 2022