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 A107458 #57 Aug 28 2024 11:51:26
%S A107458 1,0,0,0,1,0,1,1,2,2,4,5,8,11,17,24,36,52,77,112,165,241,354,518,760,
%T A107458 1113,1632,2391,3505,5136,7528,11032,16169,23696,34729,50897,74594,
%U A107458 109322,160220,234813,344136,504355,739169,1083304,1587660,2326828,3410133,4997792,7324621
%N A107458 Expansion of g.f.: (1-x^2-x^3)/( (1+x)*(1-x-x^3) ).
%C A107458 The sequence can be interpreted as the top-left entry of the n-th power of a 4 X 4 (0,1) matrix. There are 12 different choices (out of 2^16) for that (0,1) matrix. - _R. J. Mathar_, Mar 19 2014
%H A107458 Reinhard Zumkeller, <a href="/A107458/b107458.txt">Table of n, a(n) for n = 0..1000</a>
%H A107458 C. Kenneth Fan, <a href="http://dx.doi.org/10.1090/S0894-0347-97-00222-1">Structure of a Hecke algebra quotient</a>, J. Amer. Math. Soc. 10 (1997), no. 1, 139-167. [Page 156, f^2_n.]
%H A107458 Renata Passos Machado Vieira, and Francisco Regis Vieira Alves, <a href="https://doi.org/10.7546/nntdm.2019.25.3.185-197">Sequences of Tridovan and their identities</a>, Notes on Number Theory and Discrete Mathematics (2019) Vol. 25, No. 3, 185-197. Sequence (T_n) is a subsequence of this sequence.
%H A107458 Renata Passos Machado Vieira, Francisco Regis Vieira Alves, and Paula Maria Machado Cruz Catarino, <a href="https://doi.org/10.14393/BEJOM-v5-2024-69801">A note on the Tetrarrin sequence</a>, Braz. Elect. J. Math. (2024).
%H A107458 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1).
%F A107458 a(n) = a(n-2) + a(n-3) + a(n-4); a(0)=1, a(1)=0, a(2)=0, a(3)=0. - _Harvey P. Dale_, Jun 20 2011
%F A107458 a(n) + a(n-1) = A000930(n-4). - _R. J. Mathar_, Mar 19 2014
%p A107458 seq(coeff(series( (1-x^2-x^3)/( (1+x)*(1-x-x^3) ), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Jan 03 2020
%t A107458 CoefficientList[Series[(1-x^2-x^3)/(1-x^2-x^3-x^4),{x,0,50}],x] (* or *) LinearRecurrence[{0,1,1,1},{1,0,0,0},50] (* _Harvey P. Dale_, Jun 20 2011 *)
%o A107458 (Haskell)
%o A107458 a107458 n = a107458_list !! n
%o A107458 a107458_list = 1 : 0 : 0 : 0 : zipWith (+) a107458_list
%o A107458 (zipWith (+) (tail a107458_list) (drop 2 a107458_list))
%o A107458 -- _Reinhard Zumkeller_, Mar 23 2012
%o A107458 (PARI) my(x='x+O('x^50)); Vec((1-x^2-x^3)/((1+x)*(1-x-x^3))) \\ _G. C. Greubel_, Apr 27 2017
%o A107458 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1-x^2-x^3)/( (1+x)*(1-x-x^3))); // _Marius A. Burtea_, Jan 02 2020
%o A107458 (Sage)
%o A107458 def A107458_list(prec):
%o A107458 P.<x> = PowerSeriesRing(ZZ, prec)
%o A107458 return P( (1-x^2-x^3)/((1+x)*(1-x-x^3)) ).list()
%o A107458 A107458_list(50) # _G. C. Greubel_, Jan 03 2020
%o A107458 (GAP) a:=[1,0,0,0];; for n in [5..50] do a[n]:=a[n-2]+a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Jan 03 2020
%Y A107458 Cf. A001634, A013979, A078012, A135851.
%K A107458 nonn,easy
%O A107458 0,9
%A A107458 _N. J. A. Sloane_, Mar 08 2008