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 A234589 #17 Aug 31 2023 13:39:26
%S A234589 1,2,4,8,16,32,64,128,255,508,1012,2016,4016,8000,15937,31749,63249,
%T A234589 126002,251016,500064,996207,1984602,3953641,7876278,15690791,
%U A234589 31258536,62271945,124055559,247138286,492338537,980816202,1953940937,3892559256,7754593434,15448376086,30775607480,61309875581,122138964964
%N A234589 Expansion of g.f.: (1+x^6+x^7)/(1-2*x+x^6-x^7-x^8).
%C A234589 a(n) is the number of binary words of length n which have no 00010100-matches.
%H A234589 G. C. Greubel, <a href="/A234589/b234589.txt">Table of n, a(n) for n = 0..1000</a>
%H A234589 B. K. Miceli, J, Remmel, <a href="http://puma.dimai.unifi.it/23_3/miceli_remmel.pdf">Minimal Overlapping Embeddings and Exact Matches in Words</a>, PU. M. A., Vol. 23 (2012), No. 3, pp. 291-315.
%H A234589 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,-1,1,1).
%p A234589 seq(coeff(series((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Sep 13 2019
%t A234589 CoefficientList[Series[(1+x^6+x^7)/(1-2*x+x^6-x^7-x^8), {x,0,40}], x] (* _G. C. Greubel_, Sep 13 2019 *)
%t A234589 LinearRecurrence[{2,0,0,0,0,-1,1,1},{1,2,4,8,16,32,64,128},40] (* _Harvey P. Dale_, Aug 31 2023 *)
%o A234589 (PARI) my(x='x+O('x^40)); Vec((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8)) \\ _G. C. Greubel_, Sep 13 2019
%o A234589 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x^6+x^7)/(1-2*x+x^6-x^7-x^8) )); // _G. C. Greubel_, Sep 13 2019
%o A234589 (Sage)
%o A234589 def A234589_list(prec):
%o A234589 P.<x> = PowerSeriesRing(ZZ, prec)
%o A234589 return P((1+x^6+x^7)/(1-2*x+x^6-x^7-x^8)).list()
%o A234589 A234589_list(40) # _G. C. Greubel_, Sep 13 2019
%o A234589 (GAP) a:=[1,2,4,8,16,32,64,128];; for n in [9..40] do a[n]:=2*a[n-1]-a[n-6]+a[n-7]+a[n-8]; od; a; # _G. C. Greubel_, Sep 13 2019
%Y A234589 Similar to but different from A172317.
%Y A234589 Cf. A234590, A234591, A234592.
%K A234589 nonn,easy
%O A234589 0,2
%A A234589 _N. J. A. Sloane_, Jan 01 2014