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 A011922 #90 Jul 10 2025 04:32:18
%S A011922 1,3,33,451,6273,87363,1216801,16947843,236052993,3287794051,
%T A011922 45793063713,637815097923,8883618307201,123732841202883,
%U A011922 1723376158533153,24003533378261251,334326091137124353,4656561742541479683,64857538304443591201,903348974519668797123,12582028104970919568513
%N A011922 a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3) with a(0)=1, a(1)=3, and a(2)=33.
%D A011922 Mario Velucchi, Seeing couples, in Recreational and Educational Computing, to appear 1997.
%H A011922 Vincenzo Librandi, <a href="/A011922/b011922.txt">Table of n, a(n) for n = 0..100</a>
%H A011922 Christian Aebi and Grant Cairns, <a href="https://arxiv.org/abs/2006.07566">Lattice Equable Parallelograms</a>, arXiv:2006.07566 [math.NT], 2020.
%H A011922 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H A011922 Yurii S. Bystryk, Vitalii L. Denysenko, and Volodymyr I. Ostryk, <a href="http://dx.doi.org/10.13140/RG.2.2.16511.73129">Lune and Lens Sequences</a>, ResearchGate preprint, 2024. See pp. 31, 56.
%H A011922 Z. Franusic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Franusic/franusic4.html">On the Extension of the Diophantine Pair {1,3} in Z[surd d]</a>, J. Int. Seq. 13 (2010) # 10.9.6.
%H A011922 Giovanni Lucca, <a href="https://web.archive.org/web/20210621080218/http://forumgeom.fau.edu/FG2016volume16/FG201654.pdf">Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences</a>, Forum Geometricorum, Volume 16 (2016) 419-427.
%H A011922 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).
%F A011922 a(n) = (2+sqrt(1+((((2+sqrt(3))^(2*n)-(2-sqrt(3))^(2*n))^2)/4)))/3. [corrected by Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 30 2001]
%F A011922 a(n) = ((7+4*sqrt(3))^n+(7-4*sqrt(3))^n+4)/6. - _Bruno Berselli_, Jul 09 2011
%F A011922 G.f.: (1-12*x+3*x^2)/ ((1-x) * (x^2-14*x+1)). - _R. J. Mathar_, Apr 15 2010
%F A011922 Sqrt(3) = 1 + Sum_{n>=1} 2/a(n) = 1 + 2/3 + 2/33 + ... - _Gary W. Adamson_, Jun 12 2003
%F A011922 a(n)^2 = A103974(n+1)^2 - (4*A007655(n+1))^2. - _Paul D. Hanna_, Mar 06 2005
%F A011922 a(n) = (A011943(n+1) + 2)/3. - _Ralf Stephan_, Aug 13 2013
%F A011922 a(n) = A001075(n)^2 - A001353(n)^2. - _Richard R. Forberg_, Aug 24 2013
%F A011922 E.g.f.: exp(x)*(2 + exp(6*x)*cosh(4*sqrt(3)*x))/3. - _Stefano Spezia_, Dec 11 2022
%p A011922 a:= gfun:-rectoproc({a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3), a(0)=1,a(1)=3,a(2)=33},a(n),remember):
%p A011922 map(a,[$0..100]); # _Robert Israel_, Jul 02 2015
%t A011922 RecurrenceTable[{a[n] == 15 a[n - 1] - 15 a[n - 2] + a[n - 3], a[0] == 1, a[1] == 3, a[2] == 33}, a, {n, 0, 15}] (* _Michael De Vlieger_, Jul 02 2015 *)
%t A011922 LinearRecurrence[{15,-15,1},{1,3,33},30] (* _Harvey P. Dale_, Dec 04 2018 *)
%o A011922 (Maxima) a[0]:1$ a[1]:3$ a[2]:33$ a[n]:=15*a[n-1]-15*a[n-2]+a[n-3]$ makelist(a[n], n, 0, 16); /* _Bruno Berselli_, Jul 09 2011 */
%o A011922 (Magma) I:=[1,3,33]; [n le 3 select I[n] else 15*Self(n-1)-15*Self(n-2)+Self(n-3): n in [1..17]]; // _Bruno Berselli_, Jul 09 2011
%o A011922 (PARI) a(n)=([0,1,0; 0,0,1; 1,-15,15]^n*[1;3;33])[1,1] \\ _Charles R Greathouse IV_, Jul 02 2015
%Y A011922 Cf. A001353, A001075, A007655, A011916, A011918, A011920, A011943, A103974.
%K A011922 nonn,easy
%O A011922 0,2
%A A011922 Mario Velucchi (mathchess(AT)velucchi.it)
%E A011922 Recurrence in definition by _R. J. Mathar_, Apr 15 2010