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 A251653 #30 Mar 28 2025 07:59:31
%S A251653 0,0,1,0,0,1,2,4,7,14,28,55,108,212,417,820,1612,3169,6230,12248,
%T A251653 24079,47338,93064,182959,359688,707128,1390177,2733016,5372968,
%U A251653 10562977,20766266,40825404,80260631,157788246,310203524,609844071,1198921876,2357018348,4633776065,9109763884,17909324244,35208804417
%N A251653 5-step Fibonacci sequence starting with 0,0,1,0,0.
%C A251653 Doubling the entries > 1 as 1, 2, 2, 4, 4, 7, 7, 14, 14, 28, 28, 55, 55,... (offset 0) gives Nyblom's palindromic binary strings having no 5-runs of 1's. - _R. J. Mathar_, Mar 28 2025
%H A251653 G. C. Greubel, <a href="/A251653/b251653.txt">Table of n, a(n) for n = 0..1000</a>
%H A251653 M. A. Nyblom, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Nyblom/nyblom13.html">Counting Palindromic Binary Strings Without r-Runs of Ones</a>, J. Int. Seq. 16 (2013) #13.8.7, P_5(n)
%H A251653 H. Prodinger, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Prodinger2/prod31.html">Counting Palindromes According to r-Runs of Ones Using Generating Functions</a>, J. Int. Seq. 17 (2014) # 14.6.2, even length, r=4.
%H A251653 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1).
%F A251653 a(n+5) = a(n) + a(n+1) + a(n+2) + a(n+3) + a(n+4).
%F A251653 G.f.: x^2*(x^2 + x - 1)/(x^5 + x^4 + x^3 + x^2 + x - 1). - _Chai Wah Wu_, May 27 2016
%t A251653 LinearRecurrence[{1, 1, 1, 1, 1}, {0, 0, 1, 0, 0}, 100] (* _G. C. Greubel_, May 27 2016 *)
%o A251653 (J) (see www.jsoftware.com) First construct the generating matrix
%o A251653 1 1 1 1 1
%o A251653 1 2 2 2 2
%o A251653 2 3 4 4 4
%o A251653 4 6 7 8 8
%o A251653 8 12 14 15 16
%o A251653 Given that matrix one can produce the first 5*200 numbers by
%o A251653 , M(+/ . *)^:(i.250) 0 0 1 0 0x
%Y A251653 Other 5-step sequences are A000322, A001591, A023424, A074048, A124312, A124313, A122997, A135055, A135056, A145029
%K A251653 nonn,easy
%O A251653 0,7
%A A251653 _Arie Bos_, Dec 06 2014