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 A090316 #27 Sep 08 2022 08:45:12
%S A090316 2,24,578,13896,334082,8031864,193098818,4642403496,111610782722,
%T A090316 2683301188824,64510839314498,1550943444736776,37287153512997122,
%U A090316 896442627756667704,21551910219673022018,518142287899909196136,12456966819817493729282,299485345963519758698904
%N A090316 a(n) = 24*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24.
%C A090316 Lim_{n->infinity} a(n)/a(n+1) = 0.0415945... = 1/(12+sqrt(145)) = sqrt(145) - 12.
%C A090316 Lim_{n->infinity} a(n+1)/a(n) = 24.0415945... = 12+sqrt(145) = 1/(sqrt(145)-12).
%H A090316 G. C. Greubel, <a href="/A090316/b090316.txt">Table of n, a(n) for n = 0..500</a>
%H A090316 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A090316 <a href="/index/Rea#recur1">Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)</a>
%H A090316 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,1).
%F A090316 a(n) = 24*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24.
%F A090316 a(n) = (12+sqrt(145))^n + (12-sqrt(145))^n.
%F A090316 (a(n))^2 = a(2n) - 2 if n=1,3,5,..., (a(n))^2 = a(2n)+2 if n=2,4,6,....
%F A090316 G.f.: 2*(1-12*x)/(1-24*x-x^2). - _Philippe Deléham_, Nov 02 2008
%F A090316 a(n) = 2*(-i)^n * ChebyshevT(n, 12*i) = Lucas(n, 24). - _G. C. Greubel_, Dec 29 2019
%F A090316 a(n) = 2 * A041264(n-1) for n>0. - _Alois P. Heinz_, Dec 29 2019
%e A090316 a(4) =334082 = 24a(3) + a(2) = 24*13896+ 578 = (12+sqrt(145))^4 + (12-sqrt(145))^4 = 334081.99999700672 + 0.00000299327 = 334082.
%p A090316 seq(simplify(2*(-I)^n*ChebyshevT(n, 12*I)), n = 0..20); # _G. C. Greubel_, Dec 29 2019
%t A090316 LinearRecurrence[{24,1},{2,24},20] (* _Harvey P. Dale_, Aug 30 2015 *)
%t A090316 LucasL[Range[20]-1,24] (* _G. C. Greubel_, Dec 29 2019 *)
%o A090316 (PARI) vector(21, n, 2*(-I)^(n-1)*polchebyshev(n-1, 1, 12*I) ) \\ _G. C. Greubel_, Dec 29 2019
%o A090316 (Magma) I:=[2,24]; [n le 2 select I[n] else 24*Self(n-1) +Self(n-2): n in [1..20]]; // _G. C. Greubel_, Dec 29 2019
%o A090316 (Sage) [2*(-I)^n*chebyshev_T(n, 12*I) for n in (0..20)] # _G. C. Greubel_, Dec 29 2019
%o A090316 (GAP) a:=[2,24];; for n in [3..20] do a[n]:=24*a[n-1]+a[n-2]; od; a; # _G. C. Greubel_, Dec 29 2019
%Y A090316 Cf. A041264, A058168, A056949.
%Y A090316 Lucas polynomials Lucas(n,m): A000032 (m=1), A002203 (m=2), A006497 (m=3), A014448 (m=4), A087130 (m=5), A085447 (m=6), A086902 (m=7), A086594 (m=8), A087798 (m=9), A086927 (m=10), A001946 (m=11), A086928 (m=12), A088316 (m=13), A090300 (m=14), A090301 (m=15), A090305 (m=16), A090306 (m=17), A090307 (m=18), A090308 (m=19), A090309 (m=20), A090310 (m=21), A090313 (m=22), A090314 (m=23), this sequence (m=24), A330767 (m=25).
%K A090316 easy,nonn
%O A090316 0,1
%A A090316 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004
%E A090316 More terms from _Ray Chandler_, Feb 14 2004
%E A090316 Corrected by _T. D. Noe_, Nov 07 2006