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A226958 a(n) = Fibonacci(n-2)*Fibonacci(n)*Fibonacci(n+2).

%I A226958 #39 May 20 2025 10:33:13
%S A226958 2,0,10,24,130,504,2210,9240,39338,166320,705058,2985840,12649570,
%T A226958 53582256,226981610,961503816,4073004770,17253510120,73087065922,
%U A226958 309601740360,1311494081482,5555577978720,23533806138050,99690802301664,422297015715650,1788878864564064,7577812474943050
%N A226958 a(n) = Fibonacci(n-2)*Fibonacci(n)*Fibonacci(n+2).
%H A226958 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1).
%F A226958 a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4).
%F A226958 G.f.: 2*(1-3*x-x^2)/(1-3*x-6*x^2+3*x^3+x^4).
%F A226958 a(n) = Lucas(n-1)*Fibonacci(n+2) = Fibonacci(n-2)*Lucas(n+1).
%F A226958 a(n) = (1/5)*(Fibonacci(3*n)-8*(-1)^n*Fibonacci(n)). - _Ehren Metcalfe_, Mar 26 2016
%F A226958 For n >= 3, a(n) is the numerator of the continued fraction [1,..,1, 3 ,1,..,1, 3 ,1,..,1] with three runs of 1's each of length n-3 and each separated by a single 3. For example, a(5)=130 which is the numerator of the continued fraction [1,1, 3 ,1,1, 3 ,1,1]. - _Greg Dresden_, Jan 01 2022
%e A226958 a(3) = F(1)*F(3)*F(5) = 1*2*5 = 10.
%t A226958 Table[Fibonacci[n - 2] Fibonacci[n] Fibonacci[n + 2], {n, 1, 20}]
%t A226958 LinearRecurrence[{3,6,-3,-1},{2,0,10,24},30] (* _Harvey P. Dale_, Apr 10 2022 *)
%t A226958 Join[{2},#[[1]]#[[3]]#[[5]]&/@Partition[Fibonacci[Range[0,40]],5,1]] (* _Harvey P. Dale_, May 20 2025 *)
%o A226958 (PARI) a(n)=fibonacci(n-2)*fibonacci(n)*fibonacci(n+2); \\ _Joerg Arndt_, Jul 07 2013
%Y A226958 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%Y A226958 Products of 3 Fibonaccis: A065563, A056570, A220362, A110224.
%K A226958 nonn
%O A226958 1,1
%A A226958 _Ron Knott_, Jun 27 2013
%E A226958 More terms from _Joerg Arndt_, Jul 07 2013