This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245306 #24 Sep 16 2023 18:54:50
%S A245306 1,2,2,5,10,26,65,170,442,1157,3026,7922,20737,54290,142130,372101,
%T A245306 974170,2550410,6677057,17480762,45765226,119814917,313679522,
%U A245306 821223650,2149991425,5628750626,14736260450,38580030725,101003831722,264431464442,692290561601
%N A245306 a(n) = Fibonacci(n)^2+1.
%C A245306 a(n) is the product of two Fibonacci numbers.
%H A245306 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).
%F A245306 a(2n) = A001519(n)* A001519(n+1) and a(2n+1) = A001519(n)* A001519(n+2).
%F A245306 a(n) = A007598(n)+1.
%F A245306 G.f.: -(2*x^3-4*x^2-x+1)/(x^4-3*x^3+3*x-1). - _Alois P. Heinz_, Jul 17 2014
%F A245306 Sum_{n>=0} 1/a(n) = (3 + 5*sqrt(5))/6 = (5*phi - 1)/3, where phi is the golden ratio (A001622). - _Amiram Eldar_, Oct 20 2020
%F A245306 a(2n) = A000045(2n-1)*A000045(2n+1). a(2n+1) = A000045(2n-1)*A000045(2n+3). - _Chai Wah Wu_, Nov 26 2020
%F A245306 a(n) = a(-n) = |F(n) + i|^2 for all n in Z. - _Michael Somos_, Sep 16 2023
%e A245306 a(9) = Fibonacci(9)^2+1 = 34^2+1 = 1157 = A001519(4)* A001519(6)= 13*89.
%p A245306 with(numtheory):with(combinat,fibonacci):nn:=100:for i from 0 to nn do:x:=fibonacci(i)^2+1: printf(`%d, `,x):od:
%t A245306 Fibonacci[Range[0,30]]^2+1 (* _Harvey P. Dale_, Aug 05 2018 *)
%o A245306 (PARI) a(n) = fibonacci(n)^2+1; \\ _Michel Marcus_, Oct 20 2020
%Y A245306 Cf. A000045, A001519, A001622, A007598, A080097.
%K A245306 nonn,easy
%O A245306 0,2
%A A245306 _Michel Lagneau_, Jul 17 2014