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 A346513 #31 Jan 04 2022 23:44:23 %S A346513 1,0,7,19,98,387,1685,7064,30043,127071,538594,2281015,9663353, %T A346513 40933296,173398367,734523803,3111498370,13180509531,55833549037, %U A346513 236514685384,1001892323411,4244083925895,17978228112962,76156996238639,322606213292593,1366581849044832 %N A346513 a(n) = Fibonacci(n+1)^3 - Fibonacci(n)^3. %C A346513 The version related to sum of consecutive Fibonacci numbers cubed is given by A110224. %C A346513 a(n+1) is divisible by Fibonacci(n). The related quotient sequence is provided by A061646, from its 3rd term. %H A346513 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1). %F A346513 a(n) = F(n-1)*(2*F(n+1)^2+(-1)^(n+1)), n>0. %F A346513 a(n) = F(n-1)*A061646(n+1). %F A346513 G.f.: (x-1)*(x^2+2*x-1)/((x^2+4*x-1)*(x^2-x-1)). - _Alois P. Heinz_, Jul 21 2021 %F A346513 For n >= 2, a(n) is the numerator of the continued fraction [1,...,1, 3 ,1,...,1, 2 ,1,...,1] with three runs of 1's each of length n-2. For example, a(5)=387 which is the numerator of the continued fraction [1,1,1, 3 ,1,1,1, 2 ,1,1,1]. - _Greg Dresden_, Jan 01 2022 %t A346513 Differences[Fibonacci[Range[0, 26]]^3] (* _Amiram Eldar_, Jul 22 2021 *) %o A346513 (PARI) a(n) = fibonacci(n+1)^3 - fibonacci(n)^3; \\ _Michel Marcus_, Jul 22 2021 %Y A346513 Cf. A056570 (partial sums). %Y A346513 Cf. A000045, A110224, A061646. %K A346513 nonn,easy %O A346513 0,3 %A A346513 _Lamine Ngom_, Jul 21 2021