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 A382479 #14 May 20 2025 15:48:19
%S A382479 1,2,2,4,4,8,7,15,14,30,28,60,56,119,111,236,220,468,436,928,865,1841,
%T A382479 1716,3652,3404,7244,6752,14369,13393,28502,26566,56536,52696,112144,
%U A382479 104527,222447,207338,441242,411272,875240,815792,1736111,1618191,3443720,3209816,6830904,6366936
%N A382479 Number of palindromic binary strings of length n having no 6-runs of 1's.
%H A382479 Vincenzo Librandi, <a href="/A382479/b382479.txt">Table of n, a(n) for n = 0..2000</a>
%H A382479 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_6(n).
%H A382479 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,1,0,1,0,1,0,1).
%F A382479 G.f.: -(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12).
%t A382479 LinearRecurrence[{0,1,0,1,0,1,0,1,0,1,0,1},{1,2,2,4,4,8,7,15,14,30,28,60},50] (* _Vincenzo Librandi_, May 20 2025 *)
%o A382479 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(-(1+x+x^2)*(x^2-x+1)*(x^7+2*x+1)/(-1+x^2+x^4+x^6+x^8+x^10+x^12))); // _Vincenzo Librandi_, May 20 2025
%Y A382479 Cf. A251707 (bisection), A251708 (bisection).
%Y A382479 Cf. A123231 (2-runs), A001590 (3-runs), A382478 (4-runs), A251653 (5-runs).
%K A382479 nonn,easy
%O A382479 0,2
%A A382479 _R. J. Mathar_, Mar 28 2025