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 A020989 #52 Apr 10 2022 14:42:58
%S A020989 1,6,26,106,426,1706,6826,27306,109226,436906,1747626,6990506,
%T A020989 27962026,111848106,447392426,1789569706,7158278826,28633115306,
%U A020989 114532461226,458129844906,1832519379626,7330077518506,29320310074026,117281240296106,469124961184426
%N A020989 a(n) = (5*4^n - 2)/3.
%C A020989 Let Zb[n](x) = polynomial in x whose coefficients are the corresponding digits of index n in base b. Then Z2[(5*4^k-2)/3](1/tau) = 1. - _Marc LeBrun_, Mar 01 2001
%C A020989 a(n)=number of derangements of [2n+2] with runs consisting of consecutive integers. E.g., a(1)=6 because the derangements of {1,2,3,4} with runs consisting of consecutive integers are 4|123, 34|12, 4|3|12, 4|3|2|1, 234|1 and 34|2|1 (the bars delimit the runs). - _Emeric Deutsch_, May 26 2003
%C A020989 Sum of n-th row of triangle of powers of 4: 1; 1 4 1; 1 4 16 4 1; 1 4 16 64 16 4 1; ... - _Philippe Deléham_, Feb 22 2014
%D A020989 Clifford A. Pickover, A Passion for Mathematics, John Wiley & Sons, Inc., 2005, at pp. 104 and 311 (for "Mr. Zanti's ants").
%H A020989 Vincenzo Librandi, <a href="/A020989/b020989.txt">Table of n, a(n) for n = 0..1000</a>
%H A020989 John Brillhart and Patrick Morton, <a href="http://projecteuclid.org/euclid.ijm/1256048841">Über Summen von Rudin-Shapiroschen Koeffizienten</a>, Illinois Journal of Mathematics, volume 22, issue 1, 1978, pages 126-148. See Satz 9(a) page 132 and Satz 21 page 144 m_k = a(k).
%H A020989 John Brillhart and Patrick Morton, <a href="http://www.maa.org/programs/maa-awards/writing-awards/a-case-study-in-mathematical-research-the-golay-rudin-shapiro-sequence">A case study in mathematical research: the Golay-Rudin-Shapiro sequence</a>, Amer. Math. Monthly, 103 (1996) 854-869, see page 858 m_k = a(k).
%H A020989 Kevin Ryde, <a href="http://user42.tuxfamily.org/alternate/index.html">Iterations of the Alternate Paperfolding Curve</a>, see index "m_k".
%H A020989 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A020989 a(0) = 1, a(n) = 4*a(n-1) + 2; a(n) = a(n-1)+ 5*{4^(n-1)}; - _Amarnath Murthy_, May 27 2001
%F A020989 G.f.: (1+x)/((1-4*x)*(1-x)). - _Zerinvary Lajos_, Jan 11 2009; adapted to offset by _Philippe Deléham_, Feb 22 2014
%F A020989 a(n) = 5*a(n-1) - 4*a(n-2), a(0) = 1, a(1) = 6. - _Philippe Deléham_, Feb 22 2014
%F A020989 a(n) = Sum_{k=0..n} A112468(n,k)*5^k. - _Philippe Deléham_, Feb 22 2014
%F A020989 a(n) = (A020988(n) + A020988(n+1))/2. - _Yosu Yurramendi_, Jan 23 2017
%F A020989 a(n) = A002450(n) + A002450(n+1). - _Yosu Yurramendi_, Jan 24 2017
%F A020989 a(n) = 10*A020988(n-1) + 6. - _Yosu Yurramendi_, Feb 19 2017
%F A020989 E.g.f.: exp(x)*(5*exp(3*x) - 2)/3. - _Stefano Spezia_, Apr 10 2022
%e A020989 a(0) = 1;
%e A020989 a(1) = 1 + 4 + 1 = 6;
%e A020989 a(2) = 1 + 4 + 16 + 4 + 1 = 26;
%e A020989 a(3) = 1 + 4 + 16 + 64 + 16 + 4 + 1 = 106; etc. - _Philippe Deléham_, Feb 22 2014
%t A020989 NestList[4#+2&,1,25] (* _Harvey P. Dale_, Jul 23 2011 *)
%o A020989 (Magma) [(5*4^n-2)/3: n in [0..25]]; // _Vincenzo Librandi_, Jul 24 2011
%o A020989 (PARI) a(n)=(5*4^n-2)/3 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y A020989 Cf. A002450, A020988, A112468.
%Y A020989 A column of A119726.
%K A020989 nonn,easy
%O A020989 0,2
%A A020989 _N. J. A. Sloane_