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 A099367 #42 Jan 05 2025 19:51:37
%S A099367 0,1,49,2500,127449,6497401,331240000,16886742601,860892632649,
%T A099367 43888637522500,2237459621014849,114066552034234801,
%U A099367 5815156694124960000,296458924848338725201,15113590010571150025249,770496631614280312562500
%N A099367 a(n) = A054413(n-1)^2, n >= 1.
%C A099367 See the comment in A099279. This is example a=7.
%H A099367 Michael A. Allen and Kenneth Edwards, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/60-5/allen.pdf">Fence tiling derived identities involving the metallonacci numbers squared or cubed</a>, Fib. Q. 60:5 (2022) 5-17.
%H A099367 Sergio Falcon, <a href="https://ikprress.org/index.php/AJOMCOR/article/view/442">Some series of reciprocal k-Fibonacci numbers</a>, Asian Journal of Mathematics and Computer Research, Vol. 11, No. 3 (2016), pp. 184-191; <a href="https://www.researchgate.net/publication/297715665_SOME_SERIES_OF_RECIPROCAL_k-FIBONACCI_NUMBERS">ResearchGate link</a>.
%H A099367 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (50,50,-1).
%H A099367 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.
%F A099367 a(n) = A054413(n-1)^2, n >= 1. a(0)=0.
%F A099367 a(n) = 50*a(n-1) + 50*a(n-2) - a(n-3), n >= 3; a(0)=0, a(1)=1, a(2)=49.
%F A099367 a(n) = 51*a(n-1) - a(n-2) - 2*(-1)^n, n >= 2; a(0)=0, a(1)=1.
%F A099367 a(n) = 2*(T(n, 51/2) - (-1)^n)/53 with twice the Chebyshev polynomials of the first kind: 2*T(n, 51/2) = A099368(n).
%F A099367 G.f.: x*(1-x)/((1-51*x+x^2)*(1+x)) = x*(1-x)/(1-50*x-50*x^2+x^3).
%F A099367 a(n+1) = (1 + (-1)^n)/2 + 49*Sum_{k=1..n} k*a(n+1-k). - _Michael A. Allen_, Feb 21 2023
%F A099367 Product_{n>=2} (1 + (-1)^n/a(n)) = (7 + sqrt(53))/14 (Falcon, 2016, p. 189, eq. (3.1)). - _Amiram Eldar_, Dec 03 2024
%t A099367 LinearRecurrence[{50,50,-1},{0,1,49},20] (* _Harvey P. Dale_, Jul 27 2023 *)
%Y A099367 Cf. A054413.
%Y A099367 Cf. other squares of k-metallonacci numbers (for k=1 to 10): A007598, A079291, A092936, A099279, A099365, A099366, this sequence, A099369, A099372, A099374.
%K A099367 nonn,easy
%O A099367 0,3
%A A099367 _Wolfdieter Lang_, Oct 18 2004